The only thing you need to be careful about are the two-class 777s and 763s which aren't distinguished from their three-class counterparts in the timetable. However, they will be identifiable because they normally lack C/D/Z business class fare availability (see below for exception). These normally operate the Hawaii routes but have been known to show up with regularity on other routes (ORD-SFO comes to mind).

Also, you can't necessarily determine that a flight is three-class just because it has C/D/Z business class fare availability. UA assign C/D/Z availability to some two-class flights which are part of an international direct flight (identifiable by flight numbers 8xx and 9xx). This is why you might see a two-class 757 or 320 with C/D/Z availability.

Trickiest of all is the potential for the domestic leg of an 8xx/9xx flight to be operated by a two-class 777 or 763. This sucker will fool you every time - it will show C/D/Z and its a 777 so its gotta be good, right? Not necessarily. The only way to know for certain is to look at the seat map.

Having said all that, there are definitely some routes and flight numbers that are consistently operated by three-class equipment. The premium transcon routes SFO-JFK and LAX-JFK use three-class 762s, though these are considered sub-par by most (there is at the moment at least one LAX-JFK and vv operating on a 763). Most of the hub-hub routes have a few three-classers a day that are probably due to equipment repositioning.