Good question !!! One I will try to do justice to ;
I've had mine for 8 months from new and had the following problems ;
1) Alarm armed / worked ok but the "tell tale" light on the dash blinked constantly, the control unit and then the immobiliser unit were replaced . . . . . . turned out to be a single diode in the loom that was missing.
2) Drivers window the mechanism worked loose and needed tightening.
3) Doors rattled a little, the dealer replaced the door strickers with larger diameter ones (now std)
4) Slight "misting" in one of the headlamp lenses getting sorted at next service.
5) Slight coolant leak after first track day (ie after first real hard driving) suspected hose clips, apparently there are tight spots on the jubilee clips and the torque drivers at the factory stop at these tight spots so some of the hoses can be loose. Being pressure tested at next service.
Generally the soft top leaks slightly (not a problem, if standing overnight in the rain there may be one or two drips inside).
The hardtop seals "squeak", but this can be fixed with some silicone spray.
Regarding rattles etc, yep, but none that are annoying all related to the fact that it's a pretty rigid chassis, your inches from the ground with only a sheet of aluminium between you and the road there is noise from the soft top (wind).
In a nutshell if you expect the creature comforts / refinement of say an S2000 (the Honda I guess that's what it's called in the US) you will not get it with the Elise.
Essentially it's not a complicated car, the K Series (which I guess you will NOT get) is a solid unit, i've not hear of any fundamental problems. The suspension / chassis is of course what Lotus are best at, it's worth keeping an eye on the geo and finding someone who can check / set it correctly. The geo is a big part of the official Lotus servicing.
Not heard of any significant problems with electrics, again it's not that complex.
Re horror stories, roofs can be a real problem, I know a couple of people who can't use the soft tops as they leak so much, there was a bad "batch" of roofs that Lotus know about.
Indicator pods have been known to pop out at speed, which can be an interesting experience.
Don't forget this is a hand built car and they're not perfect, but that's what makes them special. . . REALLY SPECIAL !!
As long as you go into ownership with the right expectation and your eyes wide open you will not be disappointed.
Don’t forget it's a car that had one eye on the track.
Finally this is just my view of ownership, the club that i'm a member of (South East Lotus Owners Club) has an active forum, go have a look around and ask the same question there ;
SELOC
Hope this helps