For a start, they don't work like a conventional auto with a torque converter. Some folks are fine with this; others just don't like the way the car drives. That's why you must always, always, always take the car for an extended test drive before committing to anything.
Then there's the reliability issue; they don't always give trouble (some here have seen >100k miles without issues), but generally after 40000-60000 miles, parts will start wearing out. Many, though not all, will be difficult and costly to fix.
Basically, once you're out of warranty, you're just one warning light away from a potential £2000+ bill that could appear at any time, with little or no other indication that anything is wrong. At this point, if they can clear the warning light, many folks just trade them in; they almost never get fixed before being sold on; there are dozens out there right now on forecourts, just waiting for some unsuspecting punter to come and buy them, which is why I recommend anyone who does still want one to buy it new and trade it away before the warranty ends.
On the plus side, in 1.2 form, they're one of the most fuel efficient automatics you can buy - not having those torque converter losses saves you 15%-20% on fuel compared to a slushbox.