When Ed and Kelly are arguing outside the elevator the hand that Ed is holding up to his mouth to yell changes between camera angles.
While Kelly tries explaining her situation to Alara, she orders "Chardonnay" from the food replicator. The wine which appears is red, and Chardonnay is a white wine. While red Chardonnay does exist, she should have specified it in her order.
Rather than look for DNA from the birthing bucket, they could simply identify which civilisation the bucket came from.
When Ed and Kelly leave the bridge to go greet the forensic archaeologist in the shuttle bay, Kelly requests that Alara send the name of the archaeologist to their comms as soon as she has found it. When Alara discovers that the archaeologist is Darulio, the main with whom Kelly had an affair, rather than contacting Kelly or Ed via communicator as requested, she runs to the shuttle bay in an attempt to abort the shuttle docking. Had she used the communicator as requested, she would not have been too late to give Ed and Kelly a heads up on the archaeologist's identity. Had she even used the communications system to contact the shuttle bay control room, rather than run there, she would not have been too late to abort the shuttle docking.
A small Union Science-class vessel is called the Olympia SCV-183. Another Union ship, the Leviathan-class Olympia LCV-529, previously appeared in Krill (2017). No real world navy would have two ships of the same name in service at the same time, regardless of class. While the fictional Planetary Union Navy need not bound by real world laws, this is not necessarily an error in-universe, but is still an oddity.