I have walked the Washington section today, although I went the opposite way to that which I mentioned ^^^ above.
I first got on to the trackbed about 400mtrs north of Victoria Viaduct, near the junction of the former Stanhope & Tyne Railway (now the Consett & Sunderland Railway Path). At the south-western end of the site of Washington station, the trackbed is fenced-off. I had to divert to the right, onto Wilden Road, then left (Sterling Close) before turning left again onto Station Road where a path has been beaten up the embankment to the north-east of Station Road bridge.
The trackbed is then distinct, although very overgrown and narrow for some distance. Approaching the ASDA Distribution Centre, there is a fenced-off bridge over a footpath (once a narrow lane?). Only the bridge is fenced, and you have to go down the embankment, across the footpath, and back up the embankment. Again, paths have been beaten on the embankment, but they are steep.
The trackbed remains distinct, and passes under the A1231, to the site of the level crossing on the A1290 close-by the new Fire Station. The dead-straight walk continues, crossing the River Don to the site of the Follingsby Lane level crossing. Up to this point, all the track has been lifted, and I spotted a few random discarded concrete sleepers along the way.
From here, the line is inaccessible - fenced-off with no visible way around it, and "No Trespassing" signs clearly visible. So I called it a day, having walked 3.25mls of the line, according to my eTrex GPS device. Through the fence I could see a siding, with track and buffer intact, on the site of what would have been Wardley Colliery.
I didn't see any "unsavoury characters" (or anyone at all, for that matter) and no obvious sightings of discarded hyperdermics or condoms - as mentioned above. However, there were plenty of discarded plastic fizzy-pop bottles, lager cans, energy drink cans, and several sites where fly-tipping has occurred.