The nut is an issue: A low E will sit on top of the the slot for a high E, and easily get knocked out.
The same may go for the bridge saddles: That's true on my SG Special, not on my MIM Tele (both post-2000), and not on my DeArmond M75T (Schaller-alike roller bridge). This is 100% dependent on the bridge saddles you've got (you may be able to reverse the order of the bridge saddles, depending on the bridge and how handy you are).
Get that sorted, and you'll need to reset the intonation.
If you're starting to be filled with dread and horror at all this, you're in good company. Just take it to a reputable local shop (google "guitar setup [wherever you live]" and sift through forum posts) and tell them you want it set up lefty.
On the other hand, my left-handed kid sister had some kind of Yamaha ES-335 copy strung lefty for a while when we were in high school in the 80s. The intonation wasn't bad enough to bother me at the time (it would probably bug me now) and she never hit the strings very hard. But after a few months she switched to stringing it right handed and learned to play upside down. She had a better ear than me back then. That was part of it. Also, she wanted to be able to play my bass and other people's guitars.
If it doesn't bother you, don't sweat it until it does. Sooner or later it will.
I wish I had that Yamaha now.