We can't say with certainty what the anticipated reliability will be.
But... there are some things one might consider.
1. A small manufacturer of cars, will have far less resources. For example, a company like Honda may have a substantial team of people working on a window crank mechanism. They can build hundreds of them and test them continuously. Statistical analysis is done. They can spend a lot of money because they will use that one mechanism (and maybe slight variations) in different models, perhaps over 500,000 cars. It's easy to amortize your up front costs. And it's smart. Problems with your window cranks on 500,000 cars is expensive.
But Lotus can't do that. They make a lot fewer cars with a lot less resources.
2. Shock and vibration. This has a big impact... no pun intended. A car that has a soft suspension will have less problems. Period. On my stiff racing kart, I have to snug up hardware all the time. Metal fatigues. Bolts back out (we safety wire everything). Stuff gets shaken to death. The Elise is more like my kart, than a soft Buick.
3. Pushing the envelope in design. Any car that is engineered to be light will push the envelope a little. In other words, one can afford a larger margin when engineering, if weight was not a large contraining factor. But with the Elise, weight is one of the main goals. You get everything as light as possible. In some cases, we may find that was too light.
4. Historically, cars from the UK have been known to have more than a normal share of electrical problems, often attribute to the God of Lucas Electronics. The old joke, why do the Brits like their beer warm? Because the refrigerators were made by Lucas. Will this be the case with the Elise?
In reading the forums of UK Elise owners, you can get a sense of some small problems. Leakage around the soft top for example. However, some of those have for sure been dealt with by Lotus, and some will not apply to the new car anyway.
One major difference will of course be the drivetrain. For most people, this is where they have the most concern, because it's the most expensive area should there be a reliability issue. But since the drivetrain is a Toyota that has been develoepd and used in production (see point 1 above), this should be a very good thing.
So.. what does all of that mean? In my opinion, it means that I think the car will be pretty reliable. You can push it on a track and expect not to break down. But you also need to take care of it because it is a performance car, and you may find small problems that will require fixing.