The most forgiving adhesive I have used for attaching PE parts is Future. Keep in mind though that Future is really only good for PE that is attaching on one of its surfaces. It isn't good for PE that attaches on its edges. For edge attachment, CA is really the best...but CA is very unforgiving of anything but exact placement of the part. If you accidentally get even the tiniest particle of CA on some other part near where you were intending to place it, its going to stick out like a sore thumb. If you're placing PE badges though, they should have enough surface area to make Future a good choice. Its completely forgiving of mistakes because when it dries, especially on a gloss surface, it is 100% invisible. Even white glue which dries "clear" will show up in the form of a slight film or difference in sheen. It can be washed off with soap and water, of course, but that will often remove the PE with it.
I'm sure you'll get lots of different suggestions, so experiment and figure out what works best for you. I'm still fairly new to PE usage myself, so I love using Future because it doesn't show my numerous mistakes in getting it placed correctly. After its all placed, you can put a clear coat over the top of it to help seal it in and protect it. In the case of military aircraft like what I build, I use a flat clear coat over it and it evens it all out to a nice, flat finish where my mistakes in placement still are invisible.
What a great tip. I always struggle with PE. CA like mentioned already isn't very forgiving and I find PVA doesn't always hold well. I just used future to join 2 flat surface area PE parts together. Looks like it worked really well. Easy to align and it looks strong. I'll spray flat clear over it too. I'm glad I found a use for future (or whatever its called) I really don't use it much for anything else.