I've been using the Canon T2i for a couple of years now and here are some of my basic thoughts in relation to your questions:
HD DSLRs are not ideal for every situation, for instance filming a long event or presentation is not what they are best at due to the clip duration limit of as short as 12 minutes. However, for more controlled or even documentary uses, the clip duration issue is easy to work around. They are definitely not as easy to work with as traditional videocameras however, in my opinion, the advantages outweigh the challenges. Audio with DSLRs is another area that requires a lot of attention - much more than traditional videocam shooters may be used to.
I think the build qualities are generally excellent, even the lower end models like mine. Higher end models like the Canon 5Ds are used in Hollywood as "crash cams" and can withstand a lot of abuse and weather related issues.
I find them to be VERY cost effective if you compare them to more traditional videocameras with the same size sensor chips or larger. Full frame videocameras are hugely expensive (10s of thousands of dollars) and that's before you've invested in glass, stabilizers and the mountain of other accessories you end up needing. Now the latest Canon videocameras - the C300 is one - I am not including as they are more like traditional videocameras that share some of the characteristics and features of HD DSLRs but, again, at a huge price increase that leaves me shaking my head.
I recently had to turn down a job that was very ENG focused (news gathering) and my Canon T2i is not ideal for this type of run and gun and don't count on mic'ing anyone beforehand environment but there are news guys that are doing it, just not me - so what I look for are situations where I have a large amount of control, where 2nd takes are possible and where beauty shots with shallow depth of field can really be showcased.