Turing Machines: decidability and bounds checking
I can construct a machine $D$ which on input $\langle M,w\rangle$ tells if $M$ moves its head past the right end on input $w$, $D$ accepts if the head does not move past the right end of input, and rejects otherwise. As configurations of length $|w|$ are finite if $M$ ever enters same configuration of length $ \le |w|$ accept. Or if it does not repeat such configuration at some point $M$'s head will move past $|w|$ tape cells. So yes your problem is decidable.