I think Police believed they had the man who killed Karen but they had not got the evidence, so they named him as a "witness" and his picture was displayed on all news reports. They also said what he told them that he claimed to have had consensual sex with her and she left his flat at 4 AM(This claim angered a lot of people). It is highly unusual to have a witness and what he said in the media like this. I think this was a strategy by the Police, emotion was running high in Glasgow and the public were engrossed in the coverage of Karen's disappearance.
The idea was that if he was up to anything people would remember and report it to Police, it worked and I believe the footage of him buying the Barrel was the significant development that broke this case. The staff of the shop saw the picture and heard the story that she left his place at 4 AM and suddenly thought, hey I remember that guy he was in here on Sunday morning buying a barrel and maybe they thought that was odd.
Maybe he was asking odd questions as well and maybe he aroused suspicion by asking could these barrels hold corrosive substances Etc. Either way I believe getting his picture out on the media was a Police strategy that paid off. Its all opinion and of course I may be totally wrong on this.