Offset errors, gain dropping and nonlinearity are common errors I have found. Excessive supply current, not shorted to output but just enough to run at blistering hot. Inputs shorted either to offset pins or each other. Inputs that have massive leakage current eiher source or sink. Offset pins that short to the substrate. Totally open not so common, but all pins shorted ( generally after getting hot enough that it melts the solder and blisters the package, or melts the glass seal on a can or cracks the cerdip package) is common. Only if the power supply is capable enough does it blow the package top off, which is generally what happens to power opamps.