What does a reading of $12000$ Roentgen mean?

The Roentgen (R) is a measure of the amount of charge liberated by ionizing radiation per unit mass of air. 1 R is defined as the amount of radiation required to liberate $2.58\times10^{-4}\,\mathrm C$ in 1 kg of air. Almost all survey meters that measure radiation exposure in R will read out as a rate, typically per hour.

The Roentgen is only defined for air, so going from Roentgen to tissue dose isn't straight forward but with a few fudge factors, you can go from R to rad (radiation absorbed dose, 1 rad = 100 erg/g). A few more fudge factors to take into account the biological effect of different types of radiation on tissue will get you from rad to rem (radiation equivalent in man).

The Roentgen is an old unit and isn't used much anymore except by old-timers. The SI unit is Kerma (Kinetic Energy Release in MAtter), which is a measure of the energy deposited per unit mass (J/kg). When air is the exposed medium, 1R = 8.73 milligray (mGy).

Yes, there is often an implied “per hour” when referring to dose rates (a.k.a. radiation levels). Frequently in the show, a number is referred to as “Roentgen” when “Roentgen per hour” is what’s actually being discussed (ex. the 3.6 as a max on the low range dosimeter or the 15000 from the reading with the truck). The dialog does — at one point — refer to radiation levels at “3.6 Roentgen per hour” (during the phone call at the end of episode 1), which is the correct unit of measure.

The difference between Roentgen and Roentgen per hour is similar to comparing distance and speed. The first is an accumulated quantity and the second is a rate.