My roof vents are leaking, apparently from the screws (?).  What is the best way to seal these to stop the leaks?

I don't know if it is the "best" way or not, but I would remove the screws, put a touch of silicone caulk in the hole and on the screw threads. Then I would put the screws back in.

roll on

I have seen many rivets & screws sealed with a layer of caulking over the heads.  If this is the way, yours are done:

1.  Remove the old sealant to clean metal.

2.  Make sure it's clean.  Your skin leaves oils.

3.  Use a high quality sealant.  I would suggest the ureathane types of sealant.  Silicone rubber is okay, but the ureathanes seem to last longer.  Anything else is a waste of time & effort.  You might save some money in materials, but you'll have to do the job again.

OK, now that I got up there to inspect before begining the job around the vents, I saw that the sealant on seam around the perimeter of the roof is completely dried out and breaking up.  Can I/should I use the same urethene caulk around this (after scraping and cleaning away all the old stuff)  Is this part of normal trailer maintenance?  Any other seals to look for?

It is normal for things to age and wear out. Your caulk will be just fine.

I would consider it normal to need to replace caulking after a few years.

In my view of the horse trailer world it is not abnormal to fix or replace things that are worn.

Good luck.

roll on