When we encounter "real world problems" in math, one can chose different levels of detail with regard to units: from leaving them out completely up to using them everywhere.
I'd argue that both extremes have their merits and inconsistent usage of units (using them in some places but not always) is wrong and leads to confusion.
To me, the most important aspect is that units are great in telling you if a calculation makes sense - and more often than not, a calculation is right if and only if the units are right. For example, due to the units alone it is evident that distance has to be divided by time to get speed.
On the other hand, units can get hard, for example if you're solving for time.
Is there scientific research or results that is pro/contra using units in math?