Rotationally enhanced red giant stars are astrophysically interesting but rare. In this paper, we present a catalogue of 3217 active red giant candidates in the APOGEE DR16 (Apache Point Observatory Galactic Evolution Experiment - Data Release 16) survey. We use a control sample in the well-studied Kepler fields to demonstrate a strong relationship between rotation and anomalies in the spectroscopic solution relative to typical giants. Stars in the full survey with similar solutions are identified as candidates. We use vsini measurements to confirm that 50 ± 1.2 per cent of our DR16 candidates are rotationally enhanced (vsini > 5 km s-1), compared to 4.9 ± 0.2 per cent in the Kepler control sample. In both, the Kepler control sample and a control sample from DR16, we find that there are 3-4 times as many giants rotating with intermediate velocities of 5 < vsini < 10 km s-1 compared to velocities of vsini > 10 km s-1, the traditional threshold for rapid rotation for red giants. The vast majority of intermediate rotators are not spectroscopically anomalous. We use binary diagnostics from APOGEE and Gaia to infer a binary fraction of 73 ± 2.4 per cent among the confirmed rotationally enhanced giants in DR16. We identify a significant bias in the reported metallicity for DR16 candidates with complete spectroscopic solutions, with a median offset of -0.37 dex in [M/H] from a control sample. As such, up to 10 per cent of stars with reported [M/H]<-1 are not truly metal poor. Finally, we use Gaia data to identify a subpopulation of main-sequence photometric binaries erroneously classified as giants.