How to make sure a proof is correct
Leslie Lamport's paper on "How to Write a Proof" (PDF) offers some useful advice.
Lamport suggests structuring the proof formally, with each statement accompanied by its own sub-proof in terms of simpler claims. How far should one continue this refinement? Lamport says: "My own rule of thumb is to expand the proof until the lowest level statements are obvious, and then continue for one more level. This takes discipline."
Go through all the steps of the proof and check them!
This is the only way I know