The best way to go about this is to post a "Needs Maintenance" note directly on the cache page. In order to do this, click on "log this cache" and in the top dropdown menu, choose "needs maintenance." In your log, describe exactly what you know by stating facts about the log being wet, etc...whatever the case may be. This will put the owner on formal "notice" that it needs to be checked. It is necessary to give the owner a while to respond since you never know what the scenario is with that person, a month is usually the best guideline. If nothing is done after a month, there are two options. You can decide to post a "needs archived" note since the owner has not responded to the requests for maintenance, or you may also take it upon yourself to fix the cache yourself. If it happens to be nearby and it's a really great cache that is worthy of the placement, I would highly suggest the latter, if you can do it. If not, a note on the forum here might yield another local cacher that could help. It's a fine line between helping and fulltime maintenance on a cache.
It would be unfortunate to have a cache archived for the sole reason of a wet log...but sometimes it does happen.
All the scenarios are different, and it's up to you how you would like to handle it. I think it's important to keep the caches here in Maine in the best condition possible...for the pleasure of cachers here and our visitors from away.