Hi, i looked at your logo and did some things to get rid of the hairlines.
If you look to the outline version of the logo you see a lot of paths on the original (right) and less on the edited one (left).

To clean up the file i did following things:
Clean up the paths: crop the logo to the cikel
– select the cirkel path and the whole logo and in the pathfinder select crop
Clean up the colors: (to many, if you want less path, you need less colors) (less = more :-) )
Select the dominate colors and hide them, by select 1 color >> go to select > select same fill >> Object > Hide.
I did this with the blue and 4 shades of grey. All the others > sellect all > set to white.
Some of the path where part overlapping, others didn’t. So i did a combination of the Pathfinder tools Divide and Merge. At the end i selected the paths of the same color and made a Compound path of each color. (less path, easy to manage) (dont forget to delete the paths with no fill/stroke color after you apply a merge or divide)

If you going to let the logo printed, it will always be better to eliminate colors, the blue is build up in 4 colors, i made an example in the workfile with the blue build up without the yellow, your printer will apreciate it :-) even better would be replace the blue by an Pantone color.
Hairlines in PDF preview comes (mostly) from the transparency flattener and in most cases they are harmless and only visible on screen, however: some of the renderstations used by printers can enlarge those hairlines, cause they will be treathed as paths and get trapped, and you dont want that… It’s my opinion, to avoid those hairlines, edit your artwork and get rid off all the settings wich are causing flattening by applying alternative settings with the same results.
For example: The clouds in the workfile are build up in various shades of grey ( K19%), above that transparency opacity of 40 % = Flattening = hairlines… You could set the transparency opacity of the cloud back to 100% and reduce the grey to K7,6% in the colorpallet = same result = no flattening = no hairline.
Dropbox - BrightEyeBeerLogo_edit.ai