Luckily the times I've passed through Heathrow it hasn't been too bad. It's like arriving in almost any other international airport (except the best ones in Asia) and, unless you are a citizen, the wait time is expected.
That's not to say Heathrow is a good airport.
Transit to T5 always kicks me. The lines at T5 at the transit point are horrible and not well managed for the anticipated traffic. I am lucky that oneworld Emerald has saved me considerable time 2 times out of 2 that I've needed to transit to T5. I think that's an unofficial thing but I'll take it to cut the lines and use Priority Security. Last time I transited to T5, had I not been able to cut the lines I think I would've missed my connection (my total transit time was just under 3 hours).
I think the biggest issue with Heathrow (in fact, all the London airports except for LCY) is passage time between gate and border. Yes, there are travelators to cut the time and effort, but it still takes considerable time to get to passport control (or, for departures, from passport control). Then, there simply aren't enough counters at immigration (and ones that actually have agents behind them) to process plane loads of people which are certainly going to be coming for the Olympics. Perhaps the thought is that if everyone moves slower to the border control then the crowding at the immigration counters will be better controlled. However, that's the wrong thinking process and will only breed discontent.
The main thing that would worry me for Heathrow (or any of the other London airports) is how they will manage baggage. That's both inbound and outbound baggage. T5 didn't fare very well when it opened, and with the exception of weather events or strikes (which it hasn't dealt with rather gracefully), I have my doubts that it can handle baggage effectively at full stress load, when that is exactly what it has to be capable of doing. Add on top of that you're going to get a flood of tourists who will undoubtedly and shamelessly flout the baggage allowance rules, and on top of that you're going to get a lot of athletes and so on that probably need to carry sports equipment (i.e. special baggage).
Overall, I'd probably more scared about how central London will handle the influx of people for the Olympics. I know that our dear friends in London are definitely not looking forward to it. Perhaps it's a good time for Londoners to consider a vacation for a couple of weeks.