I have to agree with the TSA that carrying more than $500 or so in cash is definitely suspicious. Usually a sign of drug trafficking or other illegal smuggling (but most smuggling is in the drug trade), or possibly counterfeiting (although that's unusual).
Nonsense. Carrying a large amount of cash is a sign of nothing other than carrying a large amount of cash. And $500 is peanuts if you're going somewhere where credit and debit cards aren't in much use.
It's not against the law to carry as much cash as you want (except that you need to declare if you're bringing more than $10,000 in cash in or out of the country).
The federal civil asset forfeiture laws were amended in 2000 because they were being abused by law enforcement, and the federal circuit courts have been clawing back on the circumstances under which just carrying cash is probable cause for anything else.
That pretty much sums it up. I can't remember the last time I boarded a plane with less than $1000 cash, in my pocket. The first two times I went overseas my ATM card got eaten. Blind luck, I know, but still a good reason to carry a bundle.