Once you receive the final contract from the Vendor, you need to review the contract to see how it varies from the draft contract. Any variations may indicate a section that the Vendor did not want to show you prior to purchase.
The contract should also be reviewed to ensure all the points you agreed are included in the document. Do not take the word of the Vendor that something is not included but we will still cover the commitment. If it is not in the contract, legally it does not exist. People change in organisations and in three months time, you may find the verbal commitment has been given by someone who no longer works for the Vendor. There is no record of the agreement and your requirements cannot be met.
Another point to keep in mind, is that the Vendor is as keen, if not more so, than you to have the contract signed. There will probably be considerably more flexibility in their attitude if there is a potential delay in the signing.
If you have a separate legal or contracts area, they will need to review the document. You need to allow time for the contract to be reviewed. Hopefully any contentious issues will have been addressed when the draft contract was reviewed.