Billy,
TBH, with the exception of that and a couple other incidents I had there, I would consider Taipei to be generally safer than your typical Amercan city in terms of street crime. Back in that early period of my stay was before the change of government; after around 1987 or so, things changed, and for the most part, such things seemed to become less commonly seen openly. Many were the times I walked a couple miles in the city back to my apartment late at night, with no problems. What you really need to worry about is the traffic, if you're a pedestrian. They drive like maniacs.
Yeah, TJ is someplace to keep your radar on. I haven't been back there in decades, and have no interest in ever going back. Thanks for the heads up on Albuquerque, I've heard that from someone else, too.