When Clint and Kate are in her aunt's apartment, both of his ears are visible and unobstructed. And he doesn't have the hearing aids that were introduced in the previous episode. He needed them to be able to hear, but now he can follow the conversation just fine without them.
When Kate and Clint are shopping for medical supplies, he tells her to grab some rubbing alcohol. The two bottles of rubbing alcohol are Swan brand. But later on in Kate's Aunt's apartment, when Clint has all of the supplies on the counter/table, there is only a single bottle of rubbing alcohol and it's CVS brand.
While Kate and Clint pick up supplies in the grocery/drug store, Great Value brand toilet paper is clearly on a shelf. This is a Wal-mart generic product. There are no Wal-Marts in NYC as it's highly unprofitable for them.
Kate says that Armand has 'monogrammed' butterscotch, however 'monogrammed' means that they have initials on them. His butterscotch had his full first name.
Yes, Hawkeye does sign the word "more" incorrectly, but his hearing loss is very recent, hence so would be his learning of the sign language. As such, it is absolutely to be expected for him to make novice mistakes like that at this stage.
When Kate is texting Clint, the buttons she presses do not correspond with the message that get typed out on the screen.
When Clint and Kate are shopping for medical supplies, the shelves are full of Walmart products (Equate Sleep Aid, Great Value Toilet Paper, etc), and at at least one CVS Brand item (the Wound Closure Box that he grabs off-screen and is later seen on the the table in Kate's Aunt's apartment). - Clearly, though, they are in neither CVS nor Walmart.