When everyone is in Planet Express after the machines rebel, the coffee machine and other equipment leave Planet Express but when Fry talks about feeding themselves showing a can on the table, you can see the Coffee machine is still there on the kitchen counter.
When the Planet Express crew and Mom's sons break into the cabin to find Farnsworth and Mom in bed together, they can clearly see two sets of dentures on the bedside table in glasses. Yet immediately after, viewers see both Farnsworth's and Mom's teeth are in when they speak. Further, the glasses with dentures disappear in subsequent shots.
When Mother throws the picture against the wall it shatters to reveal that Farnsworth was the lover from 70 years prior that broke her heart, it is a photo of him as he currently appears, not the "magnificent stallion" he appears as in when he recounts the story back to Mother's 3 sons.
When Tinny Tim approaches the conveyor belt with his gift for Mom at 2:32, his crutch arm and short/bad leg are on the left side. However, they are usually on the right side.
Mom's son hands Leela a map to Mom's cabin in the Bronx. The map is clearly a map if NYC but the Bronx is north of Manhattan and Mom's cabin is shown to the east- either in Queens or Nassau County.