There is hardly a game that does not come out without problems. The Legendary Edition of Mass Effect was no exception. A new update should fix the worst problems now.
It is probably not without problems in these times. A bug in the Mass Effect: Legendary Edition caused the game to inevitably crash on launch when used with certain wireless peripherals on Xbox Series X / S. Annoying, especially since quite a few players wanted to swing back into the Normandy cockpit.
Bioware and EA have meanwhile installed an update, which is supposed to fix this problem in particular (and apparently manage it, because my version is now running again). According to Bioware, crashes can still occur in connection with a wireless headset if you switch it on or off while you are in the Mass Effect Launcher. But that should also be fixed shortly.
Other contents of the update include additional improvements to terrain textures in the first part, as well as fixes for problems with trophies and achievements. In Mass Effect 2 there are also improvements to the lighting around cutscenes as well as VFX optimizations. Problems with trophies and achievements have also been fixed in Mass Effect 3.