Software Boutique Window disappears

It would most likely had been a segmentation fault, which is where some code didn't play nice with some other code. In this case, this would most likely had been the WebKit2 library. There was a bug in the past that caused exactly what you described, which has since been fixed.

Bad installation medium could also be a possible cause of faulty installations. You can verify your downloads to be absolutely sure.

For applications, try running them through the terminal. Some also accept a -v (verbose) parameter, so you can see more inner workings of what it's doing.

ubuntu-mate-welcome --boutique -v

(In future, Software Boutique will become its own program, but it's part of :ubuntu_mate: Welcome for now.

For general system and kernel (usually hardware related) logs, check the Log File Viewer and check out syslog, dmesg and kern.log, etc.