So a few possibilities with the core file.
It could be that core file generation is disabled. If you run "ulimit -c" and it comes back with "0", then that's the case. You can run "ulimit -c unlimited" from the shell prompt, then run SlickEdit from that shell, and reproduce the crash.
Once it's generated, there are a few places it could be. The old default location is the working directory of the process when it crashed. Most of the time, this will be the root directory of your open project - the directory the .vpw file resides in.
If your version of Mint uses apport, then the file will be in /var/crash.
If it's not there, cat /proc/sys/kernel/core_pattern. This will give us either a location pattern for where the core dumps are configured to be dropped on your system, or the program that handles dumps.
If you locate the dump, we'll PM you with instructions on how to upload it to us.