- Most recent in 2023: significant problems and disruptions due to problems with the Pratt & Whitney PW1100G engines in their A320neo aircraft - https://en.wikipedia.org/wiki/Pratt_%26_Whitney_PW1000G
- Mid-air diversions: several Hawaiian Airlines flights forced to divert to different airports due to mechanical problems. One example is Flight 383 from Honolulu to Kauai and had to return to Honolulu shortly after takeoff due to unspecified issues - https://liveandletsfly.com/hawaiian-airlines-lax-diversion/
- 1994: Flight 481 experience complete hydraulic system failure en route from Maui to Honolulu - https://archives.starbulletin.com/2000/12/25/news/story3.htm...
etc.
The most common claim is that they have never suffered a jet hull loss, which is technically correct as they paid over $100 million to repair 747 VH-OJH instead of letting it be written-off:
Certainly they have a good enough maintenance program to avoid something like AS261 but everything else seems like it would involve a lot of luck.