Do Missing Placards Ground an Aircraft?

Answer: Do the missing placards detail operating limitations for the aircraft? Per FAR 91.9, "Except as provided in paragraph (d) of this section (which covers helicopter over water operations), no person may operate a civil aircraft without complying with the operating limitations specified in the approved airplane or rotorcraft flight manual, markings, and placards, or as otherwise prescribed by the certificating authority of the country of registry." 

The key phrase is “operating limitations.”

Check the FAA-approved airplane flying manual or pilot's operating handbook (POH) for details.

For example, the POH for a Cessna 172S Skyhawk stipulates that specific information "must be displayed in the form of composite or individual placards" and provides images of placards that may be found, depending on how the airplane is equipped. Among the items you find information about the position of the fuel selector during takeoff and landing, spin recovery, warnings about aerobatic (although it refers to them as acrobatic) maneuvers, etc.

Keep in mind some placards are added by the aircraft owner. For example, "Don't Put Anything on Glareshield" in a Cessna 172 didn't come from the factory but rather from a pilot who saw the interior of the windscreen of someone else's airplane get scratched up by a poorly placed iPad or headset.