The contract should identify who each of the parties are, preferable in the preamble (the introductory section). Identify parties by their full legal names, especially corporations, LLCs, and other parties that are not natural persons. One common mistake is to use a partial or abbreviated name for a corporation which leaves it unclear which entity is party to the contract.
Make it clear in what capacity the parties are signing
It should be obvious whether an individual is signing in their individual capacity or in their capacity as a representative of a corporation or entity. If an individual is signing as a representative of an organization, at the very least, the signature lines should identify the title or capacity in which their signing (ex: as "President", "Authorized Member", etc.)
Make sure an exhibits or attachments are actually attached
If a contract references an exhibit, attachment, schedule, or terms and conditions section, make sure it's actually included with the document. It's very common for an agreement to reference other documents or exhibits, but not to include them. At best, this introduces ambiguity to a contract. At worst, it eviscerates it.
Define important terms
Don't assume that others will know what you mean in the contract. Don't just use technical terms reflexively - be descriptive. Define important terms and use them consistently. Try to read the contract from the perspective of a third party who is unfamiliar with your industry or arrangement, and re-write it to be understandable.