From here, it's said that a higher gm/Id results in lower current consumption (which is usually preferred in low power operation) But what other effects does a high gm/Id have? Will it have other advantages and/or does it also have its disadvantages? How about for low gm/Id? Will low gm/Id also have its advantages and disadvantages (aside from high current consumption)?
Higher gm allows higher bandwidth, and lower thermal/random noise.
Lower gm allows smaller (less area needed) for active loads or mirrors in transconductance amplifiers. I've designed 50 nanoAmp per volt "opamps" used for simple filters in detecting lock in PLLs. Low gm was useful; I achieved that by using extreme L/W ratios. Lower gm also provides higher Von at the same IDD, thus better device matching should result.