you keep using the term “ply,” and I am assuming you mean plywood. The term “ply” in roofing has a much different meaning to us if plywood is indeed what you are meaning to say. Plies to a roofer are typically layers of felt/membrane (asphalt saturated, organic, fiberglass, etc.) used in the roof system.
Assuming you mean plywood and not ply, then my one bit of advice is to make sure the contractor uses H-clips when installing the plywood. This provides a small gap between the sheets of plywood so it can move (expand/contract). It also gives the plywood ridgitiy between the rafters. You don’t need caulking between the plywood sheets.
With regard to leaks, if the contractor is known to put down leaky roofs, I would have steered clear of them to begin with. If you are stuck with the contractor, then you can take some precautions by pay a little more for certain items. First, you could have the roofer install ice & water shield along the roof perimeter, and around any roof penetrations. This may already be priced into the roof along the eaves, so I would ask the contractor in a sly way how much ice & water shield he is going to install. His answer will be your clue as to what is or isn’t included.
Next, I would be curious if the contractor included in his bid the replacement of ALL flashings and counterflashings. Some roofers are only there to replace the shingles, and they intend on re-using the metal flashings. I would want them all replaced with new metal flashings even if it raises the total cost. Of course, in my way of thinking, the contractor should plan on replacing the flashings anyway, but some don’t.
You won’t need to remove the asphalt-based roofing cement from the chimney flashings if they are being replaced. The contractor simply needs to remove the existing flashings and install new flashings. You should also take note what kind of metal he is using for flashing. If they are using aluminum, G90 galvanized, Kynar finished galvanized, copper, etc… You should probably ask him, since you obviously won’t know the difference unless he ends up installing copper (not likely).
The most important thing you have that tells you what to expect is the proposal/contract that you signed. The proposal should outline exactly what the contract intends to do with regard to the roof replacement. If it isn’t clear and spelled out, then you should not have signed the proposal. This is one way some contractors get jobs, Company A bids the work with new shingles and all new flashings, Company B bids the shingle replacement only without new flashings. Oh, you want new flashings? Well then, that will be a change-order in the amount of $$$$. Now the cheaper roofer actually becomes the more expensive roofer!