This does not mean that the errors are ignored or that one fails to estimate them. It means that they are accounted for as best one can. It's is important to keep an explicit account of the fact that there is an error and some estimate of its magnitude.
Well yes, if you don't keep track of the errors in assumption, you don't know whether they are small enough to bury within allowable engineering error. What experience buys you is that you learn when you need to keep track of such things and when you don't. Kind of like knowing when Newtonian physics gives good enough answers and when it doesn't.
I guess the important thing is to know that there is an error out there that may need to be accounted for. Some things are more sensitive to errors than others. Typical allowable error way back when I was doing ChemE was 10% for the system. Sometimes more, sometimes less. If you had error to burn you could often take substantial shortcuts in the system model, saving time and the possible introduction of errors while doing things the long way. These days it is less of a factor due to the extensive automation of engineering computation.