If a full inspection contingency is part of your contract (there are different options), then, after careful review of the inspection report(s), you'll then draw up a repair request with your buyer's agent and submit it to the listing side. Once an agreement has been reached, the seller is responsible for having "all repairs/replacements done in a workmanlike manner". It is not necessary to always hire a licensed contractor (replacing a burnt-out light bulb is a good example here) but, in most cases, it is advisable and has to be clearly indicated by you, the buyer.
The Home Inspection Contingency Notice/Addendum has a space for
Licensed Contractor(s) and receipts: the following items enumerated from the above list shall be replaced, repaired or otherwise rectified by licensed contractor and Seller shall provide Buyer with a receipt from said contractors for such work by settlement:
Thus, before you sign the papers at settlement a copy of all repair invoices/receipts will be provided to you which serves as your verification that all agreed upon repairs have been successfully completed. In addition, the final walk-through (done within the 5 days prior to settlement) is another opportunity to verify repairs/replacements. For that reason, it is advisable to not wait until the very last minute to schedule your final walk-through. Should anything be unsatisfactory, there's time to address it and find a solution without having to postpone closing.
More often than not, the repair receipts and your final walk-through is how you verify that all repairs/replacements have been addressed.
Under certain circumstances, however, it may be smart to bring back the home inspector to help you check on all repairs/replacements. Any re-inspection costs would be yours to carry. A word of caution, however, at this time the inspection contingency has already been removed in exchange for repairs (and/or a credit), this would not serve as a second home inspection after which a new list of repair requests can be submitted/negotiated!
Sometimes it is better to negotiate a credit vs. asking for repairs but that is a topic for another day.
Silver Spring, MD Buyer FAQ: How are home inspection repairs verified?