I just took a look at it.
This indeed appears to be a valid but minor bug.
car-internal takes an unused ω∈P argument, unnecessarily, I think, because it doesn't need to access arbitrary library functions, so that argument doesn't have to be passed in.
car-internal = λεωκ . hold(ε | Ep ↓ 1)κwould be replaced with:
car-internal = λεκ . hold(ε | Ep ↓ 1)κ
Otherwise, the handling of car looks OK to me. We could have dealt with errors differently in the formal semantics, pushing them into the answer type A, but that isn't anything to address now.
Going through that, I noticed something even more minor. It appears that the definition of send uses a round paren "(" in place of a left angle bracket "<".
send = λεκ . κ(ε>
Steve