As the partner in a movie house, Parrot seems to be a hopelessly irresponsible bungler, but is ever-resourceful in avoiding effort. The 'Gloria Snootful' poster is good for a chuckle, as Gloria Swanson's overdressed De Mille society outings were ripe for sending up. When the theater's press agent (George Rowe) takes a day off to get married (with subplot of hastily obtaining the marriage license), Parrot is assigned the task of posting showbills; "Be intelligent!" his partner implores (though he MUST know it's a lost cause).
Parrot proceeds to determinedly post anywhere but where it would logically serve its intended purpose, and he seems to be a complete moron-- but an inventive one. There are predictable gags, of course, but quite unexpected ones as well. There's also the fun of watching a real southern California setting as it was over ninety years ago. Which town IS that?
The press agent's marriage license quest is a pretty good little comedy in its own right, and intersects amusingly with the bill posting. We're not really told specifically that the anxious groom IS the press agent, but it's after the news about his day off that we cut to the modest wedding scene, with his realization that a license is needed. That can be a bit confusing on first viewing, especially if the film is being run at sound speed (as it is on YouTube and the source DVD), since one has little time to ponder these points before the action has gone elsewhere.
In the days of silent comedy, there seems to have been a belief that a kick in the pants was funny, and thus if one kick in the pants was funny, more would be even funnier. Uh-huh. Mercifully, here the pants- kicking is finished early on, and most of "Post No Bills" is perfectly enjoyable. So just put your brain in neutral, and it's a pretty good ride!