For us the mayhem used to last for weeks because DST changes in different countries at different times. However, the biggest challenge was always to convey to many programmers that despite a date being in different timezones, the UTC timestamp is always the same and that timezone merely changes the interpretation of a UTC timestamp. Than there was the nuisance of different machines running in different timezone and some automatically generated cron jobs all going haywire. And then, any scripts you write to fix the issue have to wait for 6 months before they can be battle tested. It took us a good 3 DST changes to finally solve the problem and still it is quite an unpleasant hack.
No, I would not miss DST either. After all it has been more than a century since light bulb liberated us from relying on the Sun as the sole source of light.