Assuming the person ties the same knots on the left and right shoe, there's going to be differences in the postures of their two hands when they tie one shoe versus the other. These differences can range from subtle and probably inconsequential to large and possibly consequential.
The degree of difference depends largely on the overall posture of the person, and to a lesser extent on the relative size of different parts of their body. Regarding posture, if they tie their shoes by sitting down and leaning over to tie each shoe the difference in posture is almost certainly not going to be large enough to have an effect. OTOH, if they tie them by crossing each leg over the other in turn, the differences in posture will be large and possibly make a difference. Further, in that example, the foot (and by proxy the shoe) will be prone to moving during the tying process, which can make it more difficult to tie a good knot.
Regarding relative size of body parts, a person with long legs relative to the arms will generally have to adopt a more unusual posture when tying their shoes and thus be more prone to error.
The brain works best when the joints are in the middle of their range because it gets the most accurate input from the position sense (the body telling the brain where its parts are, based on information from the muscle spindles, skin and joints). I vaguely remember learning the muscles can exert more force with the joints in the middle of their range as well - something to do with the stretch of the tendons or some such - but not sure if that would be relevant to tying one's shoes since it's more of a question of precision than force.
Another issue could arise due to handedness. Everyone falls on a handedness continuum between strongly left- and strongly right-handed, with ambidextrous people in the middle. Counter-intuitively, the non-dominant hand tends to be the more precise one whereas the dominant hand tends to have more strength. In a movement where precision is key, being ambidextrous would be the ideal, and the further one is on the scale towards strongly left- or strongly right-handed the more likely the brain would have problems with executing precision movements with the dominant hand.
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