Well, my interpretation of continuity for a show is that the show maintains a consistent set of rules in addition to a general adherence to what has happened historically in the show. With that in mind;
Shaving/Haircuts/Cleanliness tend to be relative to individual characters, Glenn manages to stay completely shaven while Rick seems to be completely unshaven (up until last episode).
Every zombie's strength is relative to whatever situation its in. If its going to kill a character, the zombie is incredibly strong, if its a main character they can usually just shove it off. For example Carl had that one time where he went off alone (I think he got ice cream or something?) and was swarmed, or when Tyreese was swarmed with only a hammer, or when Glenn had riot gear on and pushed through 20ish zombies, there's no way a zombie could tackle someone to the ground, but the character's wouldn't have died in that scenario.
Car's are completely relative to the character's needs. They couldn't find a car for the sixty-mile trip to Virginia, but they found one in like ten seconds when they need one to get to Alexandria?
The length of time it takes a survivor to change into a zombie seems random, I remember reading something like the "quality of life" is what determines how long one has when bitten, but that doesn't really seem to apply to most of the show. So, for example, Jim/Bob went like a day or so without anyone noticing they were bit, but Tyreese started to become delirious after like 15 minutes, and Shane changed into a zombie in like maybe 30 seconds, whereas it took characters like Amy almost a full night.
Speed of the zombies is, again, relative. There's the scene where Otis and Shane are being chased by a horde and the horde poses a legitimate challenge to the fast-pace of Otis/Shane (granted they were limping, but the zombies were hoofing it to the point Shane feared they would catch them) whereas the group was shown recently casually strolling with dehydration with the crowd in the background barely getting close to catching up. You might be able to sell me on the idea that speed degraded over time along with their body, but their strength doesn't seem to have.
Smaller things like taking Noah out on a run and it seeming like he should be limping more considering they suggested having a surgeon operate on him, Carl's maturity kind of seems to jump around, at times he seems immature (leaving Alexandria to chase Enid, going off on his own as a way to show his independence) while others it feels like they're trying to sell him as a near adult.
Fire/Light sometimes attracts zombies other times not. So, for example the one red-head guy shoots a flair and it shows the zombies noticing it, but they completely ignore the flair that lights up the zombies head, or they're attracted to the barn during the tornado because of the fire, but then just leave I guess? Or when Morgan has the blankets over the house to avoid letting light get out (though he may have mistaken what zombies do/don't notice), but they were attracted to the cabin burning (By Daryl/Beth) and were attracted to the trash fire set by Carol(?) in Atlanta. So they clearly are attracted to fire, but then not all fire, only bonfires like Hershel's barn burning, but not like, a flair I guess.
Contaminated water sometimes seems like an issue, other times not at all. For example, they had a well that literally had a live zombie in it, and they intended to drink from the well up until the zombie split in half (like it wouldn't have open wounds?) or when shane puts the bloody knife in his mouth. So it doesn't seem to be passed orally, but then you have situations where, if I'm recalling correctly, they've been unable to use water sources because they could be contaminated? I can't recall the exact instance, but I felt like at some point this was mentioned, perhaps as the reason for having the water tanks on the prison roof?
Either way, yes some of this is sort of nit-picky, but the show sort of just makes up the rules as it goes along, rather than setting over-arching sets of ideas.