Some random feedback:
Logfind
1) 'To consider a solution as 'passed', it would need to produce output on a log file of about 5 GigaBytes in under a seconds.' - you need to firm up this requirement especially if the tool will be scored by an automatic tool
Tweetdensity
1) http://linode.interviewstreet.com/tasks/4890/response1.json
Error: Parse error on line 1:
{ tweetdensity:{
-----^
Expecting 'STRING', '}'
2) Would like more direction for using the Twitter API - you could at least link to the docs for the API route that will give me this information
3) Is there an upper limit on 'count'? I believe there is some limit to how far back you can get data from the Twitter API.
Facematch
Sigh, not going to touch this one - 'See that feature that engineers teams at Google and Facebook have spent months implementing? Yeah, do that in a few hours/days for a chance to interview with a startup!' - the very least you could do is provide some library or guidance as to what tools might be well suited for this task.
Overall
The public key stuff seems complicated and a pain. Why not use Heroku (or let me use my own VPS/ec2 instance)? Or modify the problems so that I run it locally on my machine and submit the results - for Logfind, you could provide a program that takes a seed to generate the 5GB file. When I am ready to submit, give me a seed that will expire in 5 minutes and I have to enter my output before it expires or get a new seed.