Many tests for attributes listed on the chunk-format and player.dat pages of the Minecraft wiki aren't detected by command blocks testing for them.
Here's a list of tags I've found that don't appear to ever return true, along with example commands I've tested.
Health: testfor @e {Health:20}
HealF: testfor @e {HealF:20.0}
Fire: testfor @e {Fire:-1}
Air: testfor @e {Air:300}
AttackTime: testfor @e {AttackTime:0}
HurtTime: testfor @e {HurtTime:0}
DeathTime: testfor @e {DeathTime:0}
ActiveEffects: testfor @e{ActiveEffects:[{Id:10}]}
inData: testfor @e {inData:1}
If this is a syntax error on my part I apologize, but with such commands as "testfor @e {Riding:"Pig"}" working fine, I don't see how it could be the case.
A large number of tags require you to label their tag-types, which are listed on the wiki next to the corresponding tag:
AttackTime no longer appears to exist.