If memory serves, post Challenger explosion analysis showed that the SSMEs were gimballed several degrees off nominal to compensate for the thrust venting out of the solid rocket motor. I don't know if they could've done anything (like an emergency jettison of the SRBs) had they known, but it's conceivable that had the ground controllers been trained to recognize non-nominal gimbal angles as a problem, they might've been able to do something.

Before the Columbia reentry, there was speculation in internal NASA emails as to the likely telemetry indications the ground controllers would see if there was a tile breach. Sure enough, they knew the crew was in trouble when those telemetry indications showed up. By then, it was too late to do anything.