That's fairly normal for older or more basic digital watches - they don't know anything about the year, so every four years you have to manually set them back the 29th of February. I think that people see this as a bug says something about changing expectations. Pre-digital watches generally didn't know about months either, so required manual date adjustment every other month. The framing of this manual adjustment as a bug feels like it comes from our experience of dealing with computer software all the time.
In mechanical watches, that's the difference between an annual calendar, and a perpetual calendar. Annual calenders don't take leap years into account, perpetual calenders do.
Timex Ironman bought within the last two years, almost certainly less than $20, says 3/1 Sat today. The numbers on the back might say "029 36". Or maybe "029 56". I'm sure its innards are the same as most of the other sub-$20 Ironmans.