Custom Error Message

It might have helped if you'd shown your code - that way we could highlight specific issues, but in general the format you're looking for is:

tell application "BBEdit"
try
-- your code here
on error errMsg number errNum
-- an error occurred, so tell the user
display dialog "Oops. Something went wrong. The error message was '" & errMsg & "' (" & errNum & ")"
end try
end tell

This could produce an error message like:

Oops. Something went wrong. The error message was 'File not found' (-43)

Technically the 'errMsg' and 'errNum' parameters on the 'on error' line are optional - they're only needed if you want to capture the actual error message and/or number returned by the application that the the error. For example, if you know what specific error numbers mean you could customize your action based on the errNum (some might not need reporting to the user, others might cause you to take additional action in your script, etc.).

Ahh, interesting - it appears that BBEdit's 'open location' command throws an error on its own before reporting back to the calling AppleScript.

This is something that should be passed back to Bare Bones since they are the only ones that can suppress that initial warning (maybe they can detect the fact the open was issued via AppleScript and adjust their actions accordingly).

Another option is to use a custom error message; very handy when using subroutines with try statements inside an application.

tell application "BBEdit"
try
-- your code here
on error errMsg number errNum
-- tell the user using an error dialog instead of standard dialog
error "Oops. Something went wrong. The error message was '" & errMsg & "' (" & errNum & ")"
end try
end tell

Get's a little tricky depending on how the target application handles AppleScript errors (for example, when running the script with Script Editor the error dialog happens in Script Editor, not BBEdit).

You're correct, using the error command would allow you to post a more informative error message to the user. However 'error' would still terminate the script, and I interpreted the OP's request as more wanting to intercept the error and take corrective action, which was why I just used 'display dialog' as an example.

I suppose without knowing the original intent it's hard to know which works best.