wrote:
Turns out there was a bug that managed to hit the pitot dead center on
the airplane's last flight. I wonder now if testing the pitot heater
cooked it in place.

Mmm, fried bug. Was the bug too far into the tube to see from the
preflight, or are(were?) you not in the practice of checking the tube in
your walk-around?

Two questions: during a flight test with an examiner, who is PIC?

The one making the go/no-go decision is the PIC. The one with his hands
on the controls is PIC (hint: the examinee is PIC. The examiner can tell
you to do anything, just like ATC can tell you to do anything. But you,
as PIC still make the decision whether to follow the instructions or
reject them).

Second question, was the
airplane legal without an airspeed indicator?

Instruments and equipment requirements

91.205 (d)(1)

IFR: Instruments and equipment specified in paragraph (b) of this section...

91.205 (b) (1): Airspeed indicator.

(hint: no.)

Even if the flight was NOT legal, I am not tearing up the card that
says "Instruments"

61.45 (b) (1) (i)

....An aircraft used for a practical test must have:

The equipment for each area of operation required for the practical test.

An airspeed indicator is required for most of the PTS tasks. I think you
made the right decision in aborting the takeoff, but you made the wrong
one in continuing the flight without essential equipment, and the
examiner is just as culpable for ignoring the PTS and the FARs to get a
student passed.

Another day, or another plane, perhaps, but not that day with that plane.

TheSmokingGnu