Well, try and get into the Renaissance, as youre directly next to the runway, and good shots are possible from the hotel car park and bar (which is very good), and if you can be bothered, just walk across the road to the perimeter fence, and you can get very close to the aircraft.
Weather at heathrow is totally crap right now, but you can see weather 7 days in advance here: http://www.bbc.co.uk/weather/5day.shtml?world=4583
As regards spotting spots, ill let someone else do the talking: http://www.plane-mad.com/guide_view.php?guide=lhr
If you can be bothered, see this: http://groups.yahoo.com/group/lhr/
As regards police and security, theyre pretty tense now, with routinely armed officer around, which isnt normal for the UK. A couple of times there has also been military support. So if a copper tells you to move, I would advise you do. They have plenty of very comfortable holding cells at Heathrow Central Police Station
They dont particularly like you coming up to the perimeter fence as well, so within minutes of getting there, expect to be moved on, as they patrol around the fence very thoroughly. Best thing to do is use a long lens and take photos from the hotel bar
I might have missed something out, but I hope I have helped!