I get the logon screen, most of the program loads, that is pretty much all the windows. Then I get a RecorderApp.exe panel telling me an unhandled error has occurred - which is what I used to generate the above report.
Clicking on the continue button a few more times gets me the Welcome screen. Then I seem to be in, but if it's bu**ered, it's bu**ered so am I at risk of doing harm trying to work with it in this condition?
I'll check SQL server condition when I can find my SQL server head - been a long time.

If you can get beyond the welcome screen close all the open windows then exit R6 and try again. I don't think you will do any harm getting this far. My theory is  that because the problem occurs before the welcome screen it is in opening one of the Windows which was saved from the previous session. I am hoping that by closing everything this will solve the problem, but if not we may have to edit the registry.

This is still happening.
The error message crops up after everything I try to do.
I tried a spreadsheet import just now and must have had to hit that "continue ..." button 20 or 30 times. Thankfully it was a very short list but if I have to do this hundreds of times (matching up Locations in that part of the import routine) then it's pretty much unusable.
I do have such imports stacking up - I've to import many large lists for the 2016 Dipterists Forum Kent field week before the end of March.
A fix would be much appreciated.

This looks more fundamental than a code bug. As far as John  can see from the call stack it seems to be throwing an exception around the HTML control used to show the startup info, which then gets stuck in a loop in the Windows event processing, i.e. each time the exception gets handled, it finishes by telling Windows to process the next message which causes another exception.
Reinstalling Recorder is the only thing we can suggests. A potential concern is that something else on the machine has changed (e.g. a Windows update) that might have caused the problem.

Before doing this you must make sure you have backups of the Recorder 6 system, both the database and files.

Security - You need to secure the following

1. The whole of the Recorder 6 folder
2. The whole of the User File Folder.
3. We suggest that you take a backup of the database through R6 (If this will work). Also that you detach the database using Management Studio and then take a  copy of NbnData_data.mdf   and the associated log file.

Deleting Recorder 6

You should be able to uninstall Recorder 6 through control panel. If the problem  you have prevents this then it can be deleted manually - if necessary please ask for further details on this.

Re-Install

1. Install version 6.23 which is available for download from   http://www.recorder6.info/page16.html

2. Make sure this is working the detach  the blank database using Management Studio.

3. Copy in the saved version of  NBNData_data.mdf and the log file in to the data folder of SQL Server to replace the files already there.

4. Use Management Studio to attach these to the SQl server instance (http://www.recorder6.info/page12.html has instruction  )

5. Upgrade Recorder 6 to version 6.25

6. Copy back in the contents of the User File folder.  Keep the backup of all files just in case there are problems.