If they do allow renters, find out what percentage of the complex/development is owner-occupied vs rented out. That will affect the loans you are able to get if you use conventional financing, and it also affects the desirability of the complex at resale as well as how it is kept up overall, not to mention resale value. Banks don't like complexes that have high percentages of renters and often won't lend on them past a certain level, which will obviously further narrow the pool of potential buyers once you are ready to sell.
You also need to find out what the HOA covers in terms of updates, repairs, landscaping, etc. - and what process you will need to go through to make any of the changes you want to do that are not covered by the HOA. They may only review architectural and other change requests at their monthly meetings, in which case, you will have to be prepared to carry the property for a month or three while you wait for the next meeting and they debate whether or not to let you do what you want, and the terms they will require, before you can even start. You may have to be prepared with architectural drawings, and will have to comply with any requirements they have regarding details and materials, as well as tell them which *licensed* contractor you intend to use. In the event that they require changes, you may have to wait for the next meeting for them to review the new drawings, if those are needed.
Find out if you will have to get their additional approval if for some reason you decide to (or have to) change contractors, and what will have to happen if you run into issues that require further changes that were not covered in the original application. When I upgraded my windows (and therefore the siding) in my house, for example, the building inspector wouldn't sign off on the job unless I added a front stoop instead of just the steps up to the front door, so I had jump through all of the hoops all over again to get an additional approval for that.
Additionally, you will want to know if you can make interior changes without approvals, or if you will also have to request approvals for those.
If you decide to make changes to elements that they normally cover but you want done before they schedule them, at your own expense, assuming they approve it, you will likely also become responsible for the upkeep of those elements forevermore, with that obligation passing to whomever you ultimately sell the place to. That in turn may affect whether a new buyer will want to commit himself to that property.
These caveats will definitely apply to condos and co-ops, maybe PUDS, and may or may not with single family developments, but you will want to find out.
If you make your offer contingent upon approval of all of the governing documents (as well as any inspections you need), the seller will provide them for you. They should be provided anyways as part of their routine disclosures.