This is true for every form that deals with data? If not, open the queries that the problem forms are based on (assuming they're not based solely on tables). If you cannot edit the data in query datasheet view, then the problem may be that the queries are no longer updatable due to your modifications. If that doesn't help because it's true for all forms, then it could be a rights issue as you say. Step through the code and ensure the necessary parameters are in effect. It's even possible that every form is connected to some table or query that you've modified in a way to make it non updatable. This can happen when queries are nested, wherein only one contains the problem - it will likely propagate the issue.
Nothing has changed on the network, and everyone who has a copy of the FE experiences the same issue? What about testing in the same environment (network, equipment, etc) with an unaltered backup FE copy that worked before the mods?
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.