[Adam Olsen]
Is it or is it not broken? That's all I want to know.
Then you first need to define what "broken" means to you. Anything short of a source of /true/ random numbers is "broken" for /some/ purposes. Python's current generator is not broken for any purposes I care about, so my answer to your question is "no" -- but only if I ask your question of myself ;-)
Better would be a PRNG with a much larger period..
Not really. A larger period is necessary but not sufficient /if/ you're concerned about generating all permutations of bigger lists with equal probability -- see the old thread someone else pointed to for more info on that. The Mersenne Twister's provably superb "high-dimensional equidistribution" properties are far more important than its long period in this respect (the former is sufficient; the latter is merely necessary).