I did not have a lawyer look at any of my contracts. I always deleted (1) the clause that gives the publisher exclusive rights to publish future works and (2) the clause that ties royalites and advances to previous and future works.
Sometimes I'd negotiate higher advances.
I worked with several different NY publishers. I never felt like they were trying to screw the author with fine print, abstruse conditions, etc. They use a standard contract. Authors are their stable of performers. If they get a reputation for screwing authors, they have trouble recruiting other productive authors.
Now, that's only my experience, and my most recent contract was negotiated about eight years ago. So, this isn't advice; it's only an account of my experience. Take it for what it cost you.
If you get a lawyer, get one who specializes in publishing contracts.