Part of the CVT issue was confusion amongst the dealerships as to the appropriate transmission fluid to use. This was corrected via a TSB, which instructs dealerships to use the special CVTF instead of the regular ATF used for the rest of the fleet. Most affected CVT cars should have been checked for problems due to this, already.
The other problem with Honda's CVT is that they use a start-up clutch instead of a torque converter. In other words, instead of a fluid coupling mechanism, there's a friction point where the CVT interacts with the drive wheels. With aggressive driving, coupled with the aforementioned CVTF issue, the clutches could wear down prematurely... and expensively.
Use the CVT properly (and not like a boy-racer, yo...

), and you should have no problems. I know a bunch of people who've had the CVT since launch with no issues.
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Still, these issues, along with customer complaints about transmission response (unwarranted, personally... it's fine just the way it is) and the fact that newer automatics and new engine programming that gives a fairer spread of torque provide similar or better fuel economy have lead to Honda dropping the CVT in favor of a more conventional 5-speed torque-converter automatic.
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But this won't matter to Mitsubishi drivers. The Mitsubishi CVT uses a conventional torque converter instead of clutches. In other words, it will be no more unreliable than the regular automatic transmission found in the Civic... and it's more responsive and better geared, to boot.
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RE: brands... while Honda, overall, is a pretty good brand... they have their share of issues... the horrendous fuel consumption and weak engine mounts of Gen.2 CR-Vs... (at least we didn't get the burning CR-Vs that the US did (oil filter issue), transmission durability issues on old Accords... poor rubber bushings on first-generation Jazzes... bizarre exploding windshield issues on EG Civics (as well as the rust thing). They're good, but nobody's perfect.
Of course, in this case, Mitsubishi has more points against them (with a scandal sheet too long to enumerate), but this is a brand new car and shares nothing with the old Lancer... based on world-car technology co-developed with Chrysler and Hyundai. The suspension feels perfect, the engine is great, the body is ultra-stiff... it's really a cut above the rest and a sure winner in its class for Car of The Year.
Oh, yes, the suspension. Complaining about the
old Lancer's suspension when talking about this car is like complaining about the Gen.2 CRV 2.0's fuel economy when talking about the Gen.3 CRV 2.0... it's a
completely different engine in the new CRV. Likewise, it's a completely different engine, suspension and
car we're talking about with this new Lancer.
The only worry, really, is whether the local Mitsubishi service centers can do this car justice. One can only hope that the recent recovery of Mitsubishi in terms of sales has allowed them to upgrade their service centers.