Es gibt in dem Satz einen Fehler.

English Translation

There is a mistake in the sentence.

Would/should in dem be contracted to im in this sentence??

There is no rule for that.
The use of " …im Satz/in dem Satz/in diesem Satz …" depends on the situation.
“in dem Satz” points a little bit more to a certain sentence, halfway to “in diesem Satz/in this sentence”.