Berserk Button: Spending too much money on something, buying something that can't be resold at a profit, or basically anything that costs the shop money. The time Corey spent $38,000 on a hot air balloon without knowing anything about the market for something like that or having a buyer for it lined up is a good example. Rick was seriously pissed, red-faced and yelling at the top of his lungs. Even the Old Man knew enough to stay out of it until Rick calmed down. There are a few times during the scene where Rick glances at the cameras for a split-second and you can tell he's holding himself back because the cameras are running. It'll be a cold day in Hell before Corey buys another hot-air balloon.
But I Read a Book About It: Sick and confined to bed for an extended time as a child, Rick developed a lifelong love of reading and has a sponge-like memory. While he never finished high school, he gives every indication of being self-educated to at least a Bachelor's degree level in physics and the Master's degree level in history. He is skilled at identifying whether antiques are real or not through considerable knowledge of woodcraft and metallurgy. He's also an extremely canny businessman.
Jack-of-All-Trades: According to his son and Chum, Rick knows at least a little bit about pretty much anything that comes into the shop
Jerk with a Heart of Gold: Rick comes across this way at times during deals, although it may just run in the family. This also applies in how he treats said family; he won't hesitate to call his son or surrogate son out (referring to Chumlee) for a dumb decision, but he also is a lot more tolerant of bad decisions than any normal boss would be and is generally very willing to forgive them for said bad decisions.
Grumpy Old Man: His good moods are few and far between, and he has very little patience for Rick, Corey and Chum
Odd Friendship: Is surprisingly close to Chumlee. Although, given that Chum is like one of his grandchildren because of how close he is to the Harrisons, it makes a bit more sense in a familial context.
Old Shame:invoked A tattoo with his wife's misspelled name on it.
Retired Badass: According to Rick, the Old Man was stationed on a ship involved with the Cuban Missile Crisis. At one point, his ship was staring down a Russian ship, both with nuclear missiles.
The Scrooge: Subverted in "Rebel, Rebel", where the Old Man buys a nice karaoke machine for Chum's housewarming party, while everyone else got him either cheap cooking supplies, or in the case of Rick, a candy dish that had been sitting in the store for 3 years.