For a scifi show, it has a low amount of inappropriateness BUT that doesn't mean it has none. And for a SyFy Channel show, it has a low amount of swearing BUT it still does have some. For instance, one episode has background music playing where they are repeating a swear word over and over again - but that was just for that one episode and was never done again. All in all, though it does have some suggestive things here and there, it is a light-hearted show for SyFy and appropriate for mature 13 year olds. If it's possible, perhaps parents could cut out certain scenes with Pete? They're very short and do not show much but it's still unneccesary to be there and the show could be much improved without them.
Though there are occasional deaths, they tend not to be very tragic or traumatizing. However, as a word of advice for parents, there is one tragic scene towards the end of season 3 that (if you're watching with kids under 13) may leave your kids very shaken. It's an extremely sad scene where a man dies (I don't want to reveal who, but if you'd like to read about it, go to the Warehouse 13 wiki and search for the season 3 episode "Emily Lake") and his friend is shocked by it. Other than that, with a parent's okay, violence is not too intense for occasional younger viewers.
For hard core scifi fans, it has less to do with actual *science* fiction and more to do with these 'artifacts' with special powers. It's a show more appealing to teenagers (in my opinion) but by all means doesn't mean that it's immature - simply imaginative.
I could sum Warehouse 13 up as a fun, exceptionally creative, and jolly show.