Most construction and household debris can go in. The limits come from Colorado's landfill rules and the rules at the transfer station that takes your load.
Colorado law has banned electronics from landfills since 2013, so TVs, monitors, and computers can't go in the trash. The Boulder County electronics page explains the statewide ban in plain terms.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. The Monument transfer station also refuses batteries, wet paint, tires, automotive fluids, household chemicals, propane tanks, and old tube TVs.
For paint, chemicals, and car fluids, the Town points residents to the El Paso County Household Hazardous Waste Facility, which is free for county residents.
If there's something you're not sure about, check with your account manager before you load it.