It was Halifax who had the first chance of the game when Craig Midgley fired well wide.
The Shots then had a gilt-edged chance when a back heel from Tim Sills to Nick Crittenden was delivered into the box. And as Scott Rendell aimed to get on the end of it, Steve Haslam cleared, putting the ball just past the post.
Chances were limited for both sides, although Shaymen keeper Ian Dunbavin was easily the busier of the two shot stoppers.
Aldershot skipper Steve Watson headed just wide, while another good ball in from Crittenden evaded both Sills and Dwain Clarke, and was cleared for Halifax to break forward - but home keeper Nikki Bull came out to collect.
Shaymen skipper Steve Bushell, on his first game back after injury, then broke forward and only a timely interception from Tarkan Mustafa prevented the midfielder from shooting.
Adam Quinn found his way into the referee's book for a challenge on Sills, which could quite easily have seen him shown a straight red. But the Shots failed to make the free-kick count and the sides went into the break goalless after a lacklustre half.
The second half started more brightly with Ryan Sugden crossing for Lewis Killeen to shoot, but the ball was blocked and the home side immediately broke forward, only to find Dunbavin was in equally fine form to collect from Rendell.
Sugden shot well off target before wining a free-kick. The ball was delivered into the box by Midgley and Sugden went down under no pressure and immediately appealed for a penalty, as the Shots players reacted furiously.
Bushell then headed over from Midgley's free-kick and it appeared Aldershot could also use a little target practice as Rendell shot well over.
Despite winning two late corners in quick succession, the home side failed to create anything.
In the five minutes of extra time both sides tried desperately to find a winner, but eventually they had to settle for a share of the spoils, which in truth was a point more than either side deserved.