Have you actually paid attention – do you know what paw preference your dog has, if any? Some studies suggest (1) that female dogs might be more right-pawed on average, while males tend to be left-pawed, and some studies suggest preference might be flexible depending on the circumstances. (2)
However, dogs without a significant paw preference were reported to be significantly more reactive to sounds (3) than dogs who were clearly left or right-pawed.
You might be able to tell whether or not your dog is left or right pawed (or ambidextrous) simply by encouraging him or her when they do things with their paws, such as play with toys or kongs and simply observing. Which paw holds the toy or food item down? Is there a pattern over time? If there is, this is the paw thought to be the dominant paw.
How to determine which paw preference your dog might have
Try stick something on their muzzle such as some balled-up tape and look at which paw they use to get it off. Put a blanket over their head and observe the same thing. Watch them move from a sit or stand and note which paw they move forward first.
There is another advantage in knowing which paw preference your dog may have. Dogs that are left-pawed tend to pay more attention to the left side of things (visual and sound). This is reverse in right-pawed dogs and no bias in attention appears in ambidextrous dogs.(1)
(1) Wells DL. Lateralised behaviour in the domestic dog, Canis familiaris, Behav Processes. 2003 Feb 28;61(1-2):27-35.
(2) Poyser F, Caldwell C, Cobb M., Dog paw preference shows lability and sex differences. Behav Processes. 2006 Sep;73(2):216-21. Epub 2006 Jun 2.
(3) Branson NJ, Rogers LJ. Relationship between paw preference strength and noise phobia in Canis familiaris.J Comp Psychol. 2006 Aug;120(3):176-83.
(4) Siniscalchi M, d’Ingeo S, Fornelli S, Quaranta A., Relationship between visuospatial attention and paw preference in dogs, Sci Rep. 2016 Aug 22