find non-monotonical rows in dataframe
"Quick" in terms of what resource?  If you want programming ease, then simply make a new frame resulting from subtracting adjacent columns.  Any entry of zero or negative value is your target.
If you need execution speed, do note that adjacent differences are still necessary: all you can save is the overhead of finding multiple violations in a given row.  However, unless you have a particularly wide data frame, it's likely that you'll lose more in short-circuiting than you'll gain by the saved subtractions.  Also note that a processor with matrix operations or other parallelism will be fast enough with the whole data frame, that the checking will cost you significant time.
I have a pandas dataframe with Datetime as index. The index is generally monotonically increasing however there seem to be a few rows don't follow this tread. Any quick way to identify these unusual rows?