The original scientific paper (Boyajian,et al. Where's the Flux?) reports that the possibility of equipment problems was investigated as the cause of the stars dimming, but none were found.
Planets and brown dwarfs are limited in size by gravity. It doesn't appear that either can become much larger than Jupiter. This would be far too small to account for the reported dimming incidents of 15 and 22 percent. This would require something 1/3 to 1/2 of the star's diameter.
It may be that KIC 8462852 is not what all the evidence, save the dimming, make it appear to be, a quite ordinary, stable, main sequence F type star. This doesn't seem very likely, though.

http://www.datasciencecentral.com/profiles/blogs/kic-8462852-models-of-transits[/url]

The video appears to show a ring of objects orbiting KIC 8462852 in a plane, at right angles to its apparent motion across the face of the star. If this motion represents a precession of the orbit, it seems very rapid by astronomical standards.
What could be imparting this motion to the objects? Would it be feasible for a ring-like megastructure to have what looks to be a polar orbit around the star? Could such an orbit be sustainable? Is there any possible advantage to such an orientation?

Here is a poll on the Cosmoquest forum I posted on this star being a civilization.

http://cosmoquest.org/forum/showthread.php?160297-Chance-KIC-8462852-is-ETI-site

Some news on the KIC 8462852 matter. Astronomer, Dr. Bradley Schaefer has revisited his work, which revealed an apparent century-long trend of gradual dimming of this star. He used some different 'check stars', non-varying controls, which are compared to the changes in brightness of Tabby's Star. He also added some data points, derived from the earliest and latest of the historical Harvard Observatory photographic plates for the period 1890 to 1989.

Despite these modifications. he found that the same long-term dimming trend still appeared. Currently, historical photographic plates from a European observatory are being studied, to see if they will show a similar dimming of the star.

Gradual, century-long dimming of this star renders the remaining natural hypothesis, comets, very unlikely. Literally hundreds of thousands of them, all of unusually large size would be required, all neatly aligned between KIC 8462852, and Earth.

In the news.

New study supports natural causes, not alien activity, explain mystery star's behavior

Sorry, E.T. lovers, but the results of a new study make it far less likely that KIC 8462852, popularly known as Tabby's star, is the home of industrious aliens who are gradually enclosing it in a vast shell called a Dyson sphere.

Public interest in the star, which sits about 1,480 light-years away in the constellation Cygnus, began last fall when Yale astronomer Tabetha ("Tabby") Boyajian and colleagues posted a paper on an astronomy preprint server reporting that "planet hunters" - a citizen science group formed to search data from the Kepler space telescope for evidence of exoplanets - had found unusual fluctuations in the light coming from the otherwise ordinary F-type star (slightly larger and hotter than the sun).

http://phys.org/news/2016-05-natural-alien-mystery-star-behavior.html

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The new paper by Hipke, et al attempts to negate Schaefer's work, through January, which seems to indicate a century long dimming trend in KIC 8462852. The matter is far from settled. In any case, it does not address itself to Schaefer's revised analysis, from April, which uses new check stars, and added data points, but still finds a long term dimming.

more news.

Alien megastructure? Dimming star may have less exotic explanation

A mysterious darkening star might not be home to an alien megastructure after all. Instead, the dimming that apparently occurred over the course of a century may actually have resulted from how telescopes and cameras have changed over time, researchers said.

Last fall, a star named KIC 8462852 made news when scientists found unusual fluctuations in the object's light. The star is an otherwise-ordinary F-type star, slightly larger and hotter than Earth's sun; it sits about 1,480 light-years away from Earth in the constellation Cygnus.

http://www.foxnews.com/science/2016/05/17/alien-megastructure-dimming-star-may-have-less-exotic-explanation.html?intcmp=hpff

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Observers for the American Association of Variable Star Observers (AAVSO) have recently reported interesting variations in the light output of Tabby's Star.

The first of these was reported on May 4th. The star appeared to have dimmed by about 0.5 magnitude. The second report is from May 16th. In this instance the star seemed to brighten by 6 magnitudes. Anomalous brightening in this star had not been reported before this.

If these reports stand up to scrutiny, they will offer further support for KIC 8462852 truly being the most mysterious star in the galaxy.

Please contribute to the kickstarter campaign to monitor this star
https://www.kickstarter.com/projects/608159144/the-most-mysterious-star-in-the-galaxy?token=45297e55

Observers for the American Association of Variable Star Observers (AAVSO) have recently reported interesting variations in the light output of Tabby's Star.

The first of these was reported on May 4th. The star appeared to have dimmed by about 0.5 magnitude. The second report is from May 16th. In this instance the star seemed to brighten by 6 magnitudes. Anomalous brightening in this star had not been reported before this.

If these reports stand up to scrutiny, they will offer further support for KIC 8462852 truly being the most mysterious star in the galaxy.

Mike, could you please provide a link for the May 16 brightening? I have not been able to find anything on it on the Web.

Tom; On the 18th, I posted about the very large brightening reported for May 16th. Very recently this data seems to have been removed from the AAVSO Light Curve Generator. It was presumably erroneous. In its place there is now a smaller but still apparently significant dimming, in the B band, on that date.

http://www.aavso.org/lcg

If you select the option to display 'discrepant' data, then you can see the points that have been manually removed

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Another link on our mysterious star:

A Kickstarter Campaign for KIC 8462852

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rOZZ
Music
Pictures

Another strange dip in brightness can be seen in the B-filter data on May 23rd. However, it's perhaps worth noting that all of these unexplained dips were recorded by the same observer (PXR).

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Another link on our mysterious star:

A Kickstarter Campaign for KIC 8462852

Thank you, Julie; The Tabby's Star Kickstarter campaign is still ongoing, for the next 12 days. They hope to purchase observation time at a network of private observatories, in order to watch for dips in the light output of KIC 8462852.

Observation of this star during such dimming incidents, and detailed characterization of the resulting light curves and spectra will be the means of really understanding what is taking place at Tabby's Star.
On the chance that the proposed observations just might reveal evidence of extraterrestrial intelligence at work, it would be regrettable, if they were not to take place.
The contributions of persons interested in this remarkable star are still very much needed to raise the needed 100,000 dollars. Pledged contributions will only be collected if this goal is reached.

Just a few more hours in the campaign and we are almost there.
Come on, people!

Tabby is trying to set up a discussion board on the star https://www.kickstarter.com/projects/608159144/the-most-mysterious-star-in-the-galaxy/posts/1633722

article on Tabby's Star.

Scientists Are Now Even More Confused By Potential "Alien Superstructure"

Within our own galaxy, some astronomers believe there may be a massive piece of alien technology, built to harvest energy from a distant star. The star, KIC 8462852, also known as Tabby's Star, exhibits strange behavior, flickering and dimming, that can't be explained by any known astronomical phenomena. A new, unpublished study posted to arXiv, reports the results of studying images of the star from the Kepler Telescope over the past four years. The paper shows shocking results: the star's luminosity varied, sometimes dipping by 20% over the course of the study period. Even more perplexingly, its total luminosity, or flux, diminished by 4% overall over that time.

http://www.popularmechanics.com/space/deep-space/a22220/alien-superstructure-tabbys-star/

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I am in a mood to suggest that this star may be a multi-body system with hot Jupiters, brown dwarfs, or the like orbiting closely. I find the rush to attribute what is supposedly observed to alien intelligence and profound construction projects as unwarranted nonsense. The star is quite distant and apparently cannot be closely observed optically ?