When the wooden crate first falls in the fountain in the master shot, it is clearly empty because it is floating. When the camera cuts to a closer shot, it has been weighted down and is not floating.
As Ollie falls into the fountain, the piano lands on its side. In the next shot, it's on its other side. Then when Stan falls in, it's back on its first side. This is apparent from the stenciled 'This Way Up' on the box.
Professor von Schwarzenhoffen heatedly turns the control-lever for the player piano to its left-hand (or "off") position when he storms into his house, yet the lever is in the right-hand "on" position when are starting to carry the piano back out of the room and the Professor comes back bellowing with the ax.
When the piano is chasing Ollie down the steps, the sloping side of the crate is to the right (as seen from the street). As it actually passes over him, the sloping side is suddenly to the left, then it's to the right again as it runs down the final flight.
When Oliver Hardy (twice) and Stan Laurel fall into the pond, they emerge soaking wet, but in the following scenes they have completely dried out.
The paper music-roll that is loaded into the piano is labeled "Medley of Patriotic Songs", so it would not be likely to contain the first selection of "Arkansas Traveler", which is merely a comedic country-dance jig/reel and, thus, not really in the patriotic genre of "Dixie" and "The Star Spangled Banner", which also are included on the roll.
The player piano is equipped with a large "on-off" control-lever that causes the unit to shut off when the lever is moved to the left. Yet whilst the piano is playing "The Star Spangled Banner," the Prof silences the piano by pushing its control-lever further to the right, which should not cause it to shut off.
According to the titles in the film, the events take place later "that afternoon". When Stan Laurel and Oliver Hardy eventually do get the piano into the house, the clock on the mantle reads 9:45. This cannot be accurate, because it would not be daylight at this time of day.
When Oliver Hardy first falls in the water fountain and when Stan Laurel falls down into the fountain from the second floor, water marks are visible on the walls caused from splashes during previous takes.
It is obviously a fake piano and empty packing-crate since Laurel & Hardy could never have lifted/moved either one so easily if the piano was real. (This is especially obvious in two places in the film: when they effortlessly and noiselessly slide the box out from their wagon, and when they casually lift and start to carry the piano out of the room when the ragingly-furious Professor von Schwarzenhoffen orders them to take it away).
When Oliver Hardy dives to the ground as the crate flies over him, the wires pulling it are visible.
The paper roll obviously is meant for use in a multi-instrument calliope, as it has way too many parallel (side-by-side) "simultaneously playing" holes to be used in a piano, especially to play such simple "separate-noted" two-handed selections like these; i.e., without a lot of multiple-note chords or crescendos.
The piano's control-lever is in its right-hand position when Professor von Schwarzenhoffen first hits the piano with the ax. Thus, the unit is already turned on, and so it should have been still playing; it would not have been silent and then suddenly resumed playing when the Professor hit it with the ax.
When Oliver Hardy starts walking down the steps to see the policeman and the piano crate starts sliding down the steps after him, the shadows of the camera and crew can be seen on the side of the crate as it passes by them.