I'm not sure about AMEX - I think AMEX has its own problems - and the chart-lagging problem is an old one that usually remain trivial or easy to address (depending on the cause/situation). The main problem I've been having is with L2 and the Order Bar being out of sync, often for extended periods of time. L1 (bid/last/ask) has diverged from the quotes displayed in the L2 montage, often in perplexing, annoying, inconvenient, and eventually costly ways. P&L has also been out of sync on open positions, and there've been other, apparently related problems as well.
They've been persistent enough for me to contemplate switching to a new set-up - and I say this as a longtime user and client and notorious booster of TS. Also, though I've generally had good experiences with tech support there, on this matter I received a totally unsatisfactory response.