Hard to say much about any of your three posts--each of which describe different issues with your converted files--without physically examining the actual files.
Here are some general suggestions that apply to all three:
Record locking behavior has changed a bit. So it is possible that if you have the cursor in a field on one window for that to lock the same user out of editing the same record in a different window on the same machine. You may have to commit the record on the first window before bringing up the second window to the same record.
Window management has changed a little bit, so scripts in 5.5 that call a script in another file may need editing to include a select window step to make the correct window current.
Converting older files sometimes reveals corruption that was tolerated by the older version but results in an error or different behavior in the new. You may need to check for file corruption by running a recover on your file or by using a third party application such as FMDiff.
If you can possibly afford a copy of Fmp advanced, it will be well worth the cost. You can run your scripts with the debugger enabled to spot places where the scripts go off the rails in your converted files and you can also generate database design reports that help track down external data source references, field names and such to better fix issues with your converted files.
If you haven't already, brace yourself open Manage | External Datasources.... If you have a multi-file solution like I converted from 5.5, you may find a real rat's nest of external data source references that you may need to analyze and clean up to improve the rate at which your files first open.
For more on converting FMP files, see this knowledge base article: http://help.filemaker.com/app/answers/detail/a_id/750/kw/converting