Is this boiler piping correct?

The installer said he had never done a hot water system before. He installed the heat pumps and air handlers.

I assume the pump runs continuously which is the reason for the bypass valve. I would have installed an "air scoop" at the boiler to extract any air bubbles BEFORE they got into the system. The upper air vent is merely a "second line of defense" against air bubbles but will be ineffective for the two unit heaters ahead of it.

The pump is on the wrong side of the expansion tank. The air vent should be on top of the expansion tank. There is most likely other things wrong that may be dangerous that don't show here.

The expansion tank responds to changes in the boiler due to temperature changes, NOT the pump. An air vent "on top of the expansion tank" would vent the precharge out of the tank. There should be an "air scoop" at the boiler and the air vent would be on top of IT.

The pump is on the right side of the expansion tank. Pumps should be installed so that they are pumping away from the tank because away causes no changes in head. Dan Holohans book "Pumping Away" is a must read for any hydronic system installer and especially for a lot of old timers that have been doing things the same (wrong) way for years and years.