For me there's a lot more evidence suggesting that she's mentally unwell than the fact she's faking.
- She tells the story of how her husband was killed buying her lingerie because her sex drive had been low. As a result she goes into overdrive and sleeps with everyone in the office. These are not "normal" things to do. What's more she's unashamed of it.
- She compares drugs she'd been with Pat. I'm no expert on these drugs but unless someone had been researching for some time it would be very difficult for a non-medial professional to list them as efficiently.
- Her speech about Pat's time dancing with her during the Eagle's games. For someone who loathes football she's very familiar with statistics and patterns of their games!
I don't recall Tiffany's condition actually being named. Pat has bipolar disorder, his mood swings from ecstatic and high as a kite to deeply depressed and lethargic. He's also in denial about his condition and reluctantly and erratically takes his medication - these are all classic symptoms. In his case they were only diagnosed after the confrontation with his wife.
The deception at the end had a lot more to do with Pat's mother than Tiffany. She'd wanted him to move past his wife (who she didn't believe ever really loved him), so much so she'd tell Tiffany when he was running so she could "ambush" him (perhaps she'd even supplied the Eagle information?).
For me someone faking a mental illness would be very difficult, I believe the film makers have given more clues about her honesty than any deceit. What's more I don't believe it holds true to the moral of the film - two imperfect people coming together and being happier for it.