Well, from an outside perspective, things can often seem quite obvious; that he isn't right for her, and as her close friend I (and Jane, hopefully) can understand you wanting to be protective of her and make sure she stays happy.
The first thing I'd advise, which I'd always mention anyway, although I'm sure, like you said, your relationship is completely platonic, is to take a second just to make sure you are doing this for her, and not for you because you have (previously unnoticed?) feelings for her, or don't want to lose the time you have together if she starts seeing this guy.
Once that's sorted (I'm sure it is) then I guess the best thing you can do, as her best friend, is talk to her openly about it. Don't give her instructions, just give her advice and tell her what you think of the guy (making it clear it's for her benefit may help, if there's any chance she isn't completely clear on that).
Don't tell her to not date him, that's not your place, but tell her what you see wrong with him, or if you think that's too forward and suggestive, just make her promise she'll be careful and not to do anything silly.
You want to do all this whilst still making it clear that you are there for her, and are not annoyed that she's dating who you see as the wrong guy, just concerned for her; don't give her the opportunity to see you as controlling and try to shut you out. Basically make sure you emphasis that you will be there if she needs help with anything more than the fact that you don't think she should be dating this guy.
Hopefully she'll understand and while she may not finish the guy there and then, she should take a closer look at what she's getting into, tread carefully, and know you're there if she needs you.
That's my two cents, hope there's something in there you can make use of!