Route 357 is the only route to have double-deckers Monday-Saturday, and single-deckers on Sunday...I think. The reason is on Sundays, the route goes to Whipps Cross Hospital proper rather than to the roundabout, and there's a low bridge or building which precludes deckers. Does that also make it the only route to have a Sunday extension?
Route 379, the route with the shortest distance between termini as the crow flies? (Chingford station to Yardley Lane turning circle).
I think that honour would fall to the H13, which goes from one side of Ruislip Lido to the other, taking an 11 miles detour. If there was an index of route distance relative to the distance between termini as the crow flies, the H13 would be at the top by some margin.
RV1 - only service that starts with RV

Only bus for many of the stops
Sunday frequency is same as rest of week i.e. every ten minutes
One of two routes used for wifi trials
And I believe it's the only bus to cross the thames twice (or certainly within zone 1) and is contained entirely within a single zone/zone 1
A number of bus routes cross the Thames twice in addition to the RV1 and 521 - the 33, 411, 641, R68 and N22.
I have a great interest in trivia of the London bus network - I even did a bus themed quiz at a work Christmas party which was centred on unusual features of bus routes, such as those with an express section, passing over a level crossing or through a security check

. Just about any route can be unique if too many qualifiers are put in.
Some odd occurrences on the network, excluding school and mobility routes;
Routes that serve the same bus stop twice in one trip - 265, K5, R5 and R10. The B11 also has a full loop within a hail and ride section.
Routes that do not run on Saturday - 521, X68
Routes running at 1bph or less which have a Sunday service - 146, N28, N31
Routes with trip times exceeding 2 hours - the X26 has some 130 minute trips, whilst the 25 has some PM peak trips out of London scheduled for 121 minutes, though in reality they can take up to 135 minutes
The A10 is the only TfL route that runs along a motorway - I learned that from a
recent entry on Diamond Geezer's blog
The N279 is the only night route to cross the M25
At the moment, no route has a higher PVR at night than it does during the day - the N29 is closest, requiring only 5 less buses than the 29. However, this will change if the N35 gets its rumoured weekend frequency increase to 7.5bph. This would be due to various factors, primarily the schedule having an unreasonable level of slack time built in - I was on one that was 17 minutes late at Shoreditch, yet reached Clapham Junction on time.