When I refer to nested set model I mean what is described here.
I need to build a new system for storing \"categories\" (I can\'t think of better word for it) in a user
Yes it is a limitation of the nested set model, since nested sets are a pre-ordered representation of a hierarchy. This pre-ordering is the reason that it's so quick for reads. The adjacency model, also described on the page you link to, provides for the most flexible sorting and filtering but with a significant performance impact.
My preferred approach for inserts and moves in a nested set is to handle the affected branch as in the adjacency model: Get a list of the new siblings; find the right place in the list for the new node; and construct the required update statements (that being the bit where you really have to be careful). As for changing your ordering criteria: It's a one off batch job, so you can afford to blow some RAM and CPU on it, the most flexible answer would be to break the nested set representation down into an adjacency representation and rebuild the nested set from the adjacency based on new criteria.