I’m not sure about the cartridge that had its top off. Can you get the top back on very securely? It might interfere with the plunger mechanism inside that’s supposed to advance toward the seal end whenever a dose is drawn.
I avoid injecting any excess back into the cartridge. I can usually draw up only a drop or two extra, pull the needle out of the cartridge and expel the excess drop or two onto a tissue. My hope is that by doing this I'm avoiding (possibly) contaminating the insulin with syringe lubricant. Just before I push the needle through the seal I put firm pressure on it to drive out as much air from the hollow needle as possible. That helps to limit the size of any air bubble I get in the syringe. Beyond these precautions I try not to worry about it.
Do you hold directly upright or at an angle?
I'm holding the syringe at an upward angle (above horizontal) when inserting the needle into the cartridge. I shift position so the cartridge is close to vertical above the syringe while drawing up the insulin, I pull out the needle and then hold the syringe on an angle above horizontal while I expel the excess to to get the dose I want. I do all this over a white tissue with a bright desk lamp nearby so I can see the insulin level relative to the syringe marks as clearly as possible. I also wear a pair or drugstore reading glasses in a higher magnification than I'd need just for reading.