I was recently doing a batch of beer and for some reason the temp of the beer after I put it in the primary fermentation bucket wasn't low enough to pinch the yeast right away. I left the top off of the bucket a little bit to try and cool it faster but it was "exposed" for probably about an hour at least. My question is will this mess up the beer? or should it be ok.
Most likely it will turn out just fine, but you did add risk of infection keeping the lid off for a while. In future you should keep the lid on it, just to keep any wild organisms from flying into the beer and causing infection. I myself will often brew in the evening then let the beer cool overnight, with the LID ON, then pitch the yeast the next morning, with very good results and no infections.