In the 59th minute of a lack-lustre match, City midfielder Lee Crooks tried a close-range back-heel in a crowded goalmouth that Gottskalksson somehow pushed onto his crossbar.
It was one of the few highlights of a game in which both sides seemed content with a point.
The Bantams were without their suspended leading scorer Dean Windass, and they clearly missed their 12-goal striker.
They managed only two efforts on target in the whole match.
The nearest that Torquay came to a goal was a first-half header by midfielder Kevin Hill.
His effort from Craig Woodman's 28th minute corner was bravely parried by Bradford keeper Paul Henderson.
All the stars were in defence, with Torquay's on-loan centre-back Paul Robinson and Bradford's Mark Bower outstanding.
The Gulls had beaten promotion-chasing Brentford 3-1 at Griffin Park on Boxing Day with a hat-trick from Leon Constantine, but the former Peterborough striker was never in that sort of form.
Wing-back Lee Canoville and striker Tony Bedeau should have done better with a couple of second-half chances, but Bower's 64th minute challenge on Bedeau was just enough to force him to shoot wide.
Bradford manager Colin Todd tried a couple of substitutions to break the stalemate, but Torquay boss Leroy Rosenior kept his substitute powder dry, apparently happy with a draw.
City substitute Danny Forrest thought he had snatched all three points for the visitors in the 89th minute, but his right-foot volley was disallowed for offside.
Moments earlier Canoville had a left-footed shot held under his bar by Henderson - Torquay's only effort on target in the second half.