... as proposed by Jeri Ellsworth: the "Jones", after EEVblog's Dave Jones.
As with all SI units, we must define it in terms of base units, so I propose this:
1 Jones = (# of complaints about a topic) * (sum of levels of annoyance caused by said complaints weighted by exposure frequency to causative events, in seconds between exposures) * (# of people likely to be exposed to your ranting)
Obviously, the level of annoyance varies from person to person; I imagine a level 1 annoyance ("mild eye rolling followed by repetition of action until desired result is achieved") for a more patient colleague might be a level 5 annoyance to me ("loud sigh with posture change and muttered profanity") and could rank to a level 100 for someone else ("widely distributed internet video rant with attendant behavioral change and increased probability of property damage to exact retribution on an inanimate object").
As a practical example I'll float my issues with OrCAD- there are five things which cause me pain every day with OrCAD, three level two issues ("eye rolling with quiet sigh") and one level 6 issue ("profanity audible but not comprehensible to workers in adjacent cubes") and one level 50 issue ("loud cursing and banging of mouse on desk"). Weighted, I'd say I get one level two event every 60 seconds of OrCAD usage (.033), one level 6 issue every 300 seconds (.02), and one level 50 issue every 3600 seconds (.014), for a total weighted annoyance of .067. At best, normally, about four people are exposed to my ranting; thus my irritation with OrCAD is about 5*.067*4 = 1.34 Jones.
The nature of this is such that it is similar to the Schmidt Sting Pain Index- individual preferences and tolerances will affect the outcome heavily, as does personal audience size (clearly, Dave has a much bigger audience than I do).