Such a computer program would be as intricate as the proofs it is expected to verify, and is subject to the same human error. There cannot be certainty of correctness of a proof without certainty of the correctness of the proof-checking software. Could the program check itself?
Proof checkers are not nearly as intricate as proofs. You can write a small proof-checking core which you'd have to verify once (or trust). Then you could build checkers (compilers actually) that take higher-level proofs and translate them into the lower-level proofs that the core can check. By analogy with computers, the instruction set of a simple RISC processor can be much simpler and more straightforward than the programs that it runs. The proof-checking core could check itself, but would you believe it? (If a liar tells you he's not a liar, ...) Russ