In "Opie and the Spoiled Brat", there's a nice contrast between how Opie cries and how Arnold cries. Opie is pretty straight-forward with his feelings, not so good at faking them. So whenever he "cries", it comes out sounding annoying, loud and whiny, because he's not really feeling sad or hurt. So it's too easy for grown-ups (especially his father) to be irritated and not give him what he wants. Arnold on the other hand knows how to fake his emotions to get what he wants. His "cries" are more emotional and natural-sounding. So it's easier for him to sound sympathetic (especially to his own father, who believes his son is just sensitive).
In “Three Wishes for Opie”, Opie makes three wishes on Barney’s lamp, and they all come true. Not having been told the final wish, Barney makes a conclusion based on the words Opie uses and thinks he wished for Andy and Helen to get married, but it turns out that was not what Opie wished for. However, they do get married in the first episode of Mayberry R.F.D. So even though that wasn’t really one of Opie’s wishes, it ended up coming true as well.
Barney's inability to handle his gun properly. For his own sake, thank God he has such terrible aim, otherwise he's sure to have blown his foot off all the many times it's accidentally gone off when returning it to its holster... but in other cases, it's hard not to think about what kind of fatal consequences there could as the result of Barney's itchy trigger finger if somebody were in the wrong place at the right time.
This is exactly why Barney only carried one bullet in his shirt pocket and kept the chambers empty unless he was in a situation where the gun needed to be used. If Andy was around, Barney was supposed to ask permission to put the bullet in. Which would seem humiliating if Barney didn't know full well that it was a good idea.
Mayberry is implied to have a few thousand residents. They have a single sheriff, one deputy, one car and only two jail cells. If the town were less peaceful, Andy & Barney would be overworked, understaffed and would have nowhere to store criminals, let alone how understaffed and underequipped they are to handle emergencies. If anything, the town should've had multiple lawmen, three or four cars merely for patrol and much more space to detain criminals, not to mention a stock of emergency supplies.
There is stated to be a shed behind the courthouse that might contain emergency supplies, but the rest of this is definitely true. This was probably done for pragmatic reasons, to avoid having too many characters.
