No, it does not. Please, don't make it seem harder than it needs to.
99% applications, if you don't do anything stupid you are completely fine.
If you care for precision so much the last digit make difference for you you are probably one of very few cases. I remember somebody giving an example circumference of solar system showing uncertainty of the value of Pi available as FP to cause couple centimeters of error at the orbit of Pluto, or something like that.
(Edit: found it: https://kottke.org/16/03/how-many-digits-of-pi-does-nasa-use)
Most of the time floating point input is already coming with its own error, you are just adding calculation error to the input uncertainty. But the calculation error is so much smaller than in most cases it is safe to ignore it.
For example, if you program a drone, you have readings from IMU which have not nearly the precision of the double or even float you will be working on.
There is also various techniques of ordering the operations to minimize the resulting error. If you are aware which kinds of operations in which situations can cause huge resulting error it is usually very easy to avoid it.
Only very special case is if you try to subtract two values calculated separately and matching almost exactly. This should be avoided.
