So, the little corncob pipe I bought is filtered. I went by the drugstore on my lunch hour and wasn't expecting a big selection or whatever and this was the only corncob they had.

Is filtered better? Are there any advantages or disadvantages?

The MM I bought had filters as well.  However, I've never used a filter - just personal preference.

Personal preference. I use the filters to prevent gurgling as they tend to soak up moisture.

My understanding of filters on pipes is mostly to keep tobacco or ash from getting into your mouth. I have never yet smoked a cob so have no personal experience. Some others on the forum have said that they don't use the filters, or will drive a hole through the filter with a nail or something to increase draw and still keep the tobacco where it belongs.

If it's a straight stem, leave it in.  If it's bent, take it out and forget it was ever there.

I have many cobs, and most of them require filters, but I don't really like to use filters because I think they adversely affect the draw.  However, leaving the filters out entirely allows for a draw that is too loose for my liking and allows bits of tobacco and moisture to enter my mouth.  Therefore, what I do is take the filter and knock down the paper baffles inside using the pick on my pipe tool.  I simply run the pick through the filter.  This allows for a better draw that isn't too loose or too tight, and the filter still absorbs moisture.  Best of both worlds.  Give it a shot.  It's the best solution I've found.