I used to work for a union. Now in grad school, live with the grad student union treasurer.
1. your pay is very pathetic even for TAs.
2. You can find how much your officers and staff are getting paid here: http://www.dol.gov/esa/olms/regs/compliance/rrlo/lmrda.htm
At my school, officers get a $50 honorarium month, and staff get nonprofit compensation (low pay, decent benefits, and the thanks of thousands).
3. Some one described them as a "mob of idiots." A democratically run organization of graduate students is a "mob of idiots"? What does that make the United States?
4. Management gets the union they deserve. The big 3 have disfunctional management so they get a disfunctional union as well.
5. The Big 3 have been pissing away all their profits while ignoring their building obligations for decades. It's management's job to make sure the budget works. You don't get paid to make those decisions.
6. It's a matter of priorities. You aren't a priority (and a football stadium or refurbished admin offices are) unless you make yourself one.
7. The time to start worrying about this is way sooner in the bargaining process. Don't need to be on the negotiating team, but know who they are and tell them what you do and don't want. If you don't participate, don't expect to get what you want.
8. Union internationals typically have very little control over union locals. SEIU being the exception.
9. There are crap unions, though they are far rarer than the WSJ editorial page would have you believe. Unions with active membership are almost never corrupt, self-serving or mismanaged, just like any healthy democratic organization.
10. I have noticed a pattern of common but very short strikes in academia. I suspect Presidents feel they have to demonstrate fiscal restraint, but the vast majority would much rather move on and get back to education. Except corrupt self-serving bastards: http://en.wikipedia.org/wiki/Stephen_Joel_Trachtenberg
Hilarious and sad note: your strike pay is equal to your TA pay. This is very uncommon.