None whatsoever
For many years I have had revolvers, since that was all I was allowed to carry as an officer.
For just as many years I have shot .38 Special out of .357's with no observable problems. I used my L-frame for years in competition using .38's and it is just as accurate now as it was then, even after pushing some .357's through it as well.
As another person said, you need to keep the cylinder clean, but you have to clean any guns if you want to keep them running year after year after year.
No, go on an shoot .38's in a .357. It is fun, not as much recoil, and easier on the wallet (especially if you reload). Everything shooting should be about.
Oh, and if you don't reload now, get one of the Lee Loaders, the manual ones that have everything in a little box, and start having fun learning how to reload. When you then get into it big time, then get a press and sell the loader. That's the way I started, 30 years ago.
The Doc is out now.