Is there a problem if I don't complete sets properly when lifting weights?
Let me explain what I mean.
From what I’ve learned online, sets will normally look like this (just to give an example): 30lbs, 8 reps X 4 sets.
What happens is I might do set #1 perfectly Ok, but when I go for set #2 I cannot complete 8 reps so what I do is grab the 25’s and do 10 reps to reach fatigue. After that, for set #3 I might be even weaker so I have to lower the weight to 20lbs and do 12 reps to feel like I’m actually doing something. The issue I face is that I never have the strength to finish the set properly so I need to go lower and do more reps instead.
Will this affect my muscle growth? Should I just go for lower weight in the first place so I manage the 4 sets?
You need longer rest periods between sets. If you need to take 5lbs off the bar, that's probably okay, but don't do it more than once.
Look into taking creatine if you don't already, it will help you bang out those last few reps.