Other mistake: When Harry spits baby food on the baby (the camera lens in actuality) in retaliation for the baby spitting food on him and Tommy, Joseph Gordon-Levitt breaks character and laughs uncontrollably and looks at and gestures to off-screen crew members a couple times. (00:06:25)

Continuity mistake: When the baby Is in the ball pit you can see that he is at the edge. When they show him again he is in the middle, the last time they show him he is at the edge again.
Answer: No, the IRS cannot make you pay taxes during years in which you had no income but this family hasn't reported any income for years. You are still required to report your income every year, and if you fall below a certain threshold you don't pay federal income taxes. The IRS is assuming they are humans who have a house and careers but they have only filed taxes for a couple years (if at all). To the IRS it looks like simple tax evasion.
BaconIsMyBFF