hi lizc
I suffer from neuropathy too (although it's better now than it was a year ago, thanks I believe to reduced carbs) and for sure I have become clumsier as a result. Not tripping and falling over, but very much less lightfooted because my feet and legs hurt every day, so therefore, not liking pain very much, your movements start to become slightly unnatural.
Thankfully as my overall blood sugar levels have come down a bit the pains have gotten less, and for long stretches of time now (during the day) I'm hardly aware of any problems in my feet and legs.
However I too started suffering from dizziness back in May (but that too has gotten a bit better now) and it had nothing to do with low blood pressure as my useless doctor suggested - once after I nearly keeled over I had the presence of mind to test myself with my Boots bp meter - completely normal.
Yours is the first post I've seen suggesting a link with dizziness and neuropathy and I must say I'm inclined to believe your nurse. Diabetes has all kinds of miseries in store for us, even if our levels are pretty good most of the time (as mine seem to be - last HB1A 6.1).
Thank you for sharing this, and good luck with everything.