What should I consider when burying standard coaxial cable between the local pole and my house?
If you want to bury the cable directly in the ground then you need to use direct burial-grade cable and not "standard" cable, otherwise you need to use conduit.
First you need to consider the distance to the poll. Depending on the distance and use of the cable, you might be able to use RG6, but you also might need to use RG11.
You want to bury it deep enough that you won't cut it with a shovel should you do any yard work. They are usually a couple feet deep, but it depends on climate and location.
Make sure to call your utility company (usually your gas company) and have them come out and mark all burried cables/gas lines BEFORE you start digging - the last thing you want is to break a gas line or an electrical feed (ZAP!).
Leave yourself plenty of slack (service loops) at both ends of the cable. Overtime the ends will get cut and replaced over and over, and you need some extra cable allow for this.
You might want to check to see if your cable provider will even allow this, often they handle the last-mile connection to your demark. Because cable is "shared", a crummy installation on your end can cause issues for other customers.
Depending on your climate one thing you'll have to consider is frost/ice heave. I live in Ohio so we have to dig down a number of inches (not sure what code for cable is but I know for deck posts it's 32 inches).
I'm not sure if ice/frost will damage a cable but most likely it would over time.
The cable from the pole to your home typically belongs to the cable company. Their demarcation point should be the outside of your home. They typically install a temporary line to get your service active and make sure your TV/internet works inside, and then have the land marked for utilities and get some cheap labor to bury the line with conduit. They don't want to wait for the underground lines to be marked to get you back up, and they don't want to pay the more expensive technician to dig a trench, so it's two separate jobs done at different times.