I just bought a uberti .357. I want to know if I can mess up the gun by shooting to many .38 rounds out of it.

Nope.

You should use at least the .38 +P rounds. They are cheaper than the .357 rounds, and work just fine in .357s, and they also hit harder than standard .38 ammo.

A lot of people shoot .38, or .38 +P, rounds through their .357s for target practice, or even for self defense to have more manageable recoil.

As stated above....Fire away with all the .38spcl ammo you want. Be sure to clean the cylinders though because the .38spcl round has a slightly shorter overall length than the .357mag and over time (without cleaning) you will develop a powder residue ring that may inhibit the .357mag from sliding all the way into the cylinder.

You would have to pretty much absolutely neglect the gun for that to happen but I've seen some pretty gnarly guns in my day where I don't think they were cleaned even once.

Keep it clean....shoot 38spcl +P38spcl or .357mag all you want.

It won't hurt. You may get the previously mentioned burn ring if you don't clean the cylinders. And you don't need to shoot +P ammo either. regular 38s will be fine.

The .38 Special case is a little shorter and has a substantially lower chamber pressure than a .357 Mag. Shooting .38 Specials will be easier on the firearm vs. shooting a steady diet of magnums. One thing to AVOID is shooting lead bullets and then shooting jacketed bullets without first cleaning the firearm to get all the lead fouling and residue out (barrel, forcing cone, etc.).