http://assets.ibc.ca/Documents/Brochure ... FAQ-ON.pdf
Insurance companies have three categories: minor, major and serious. Dirty plate would be under the minor category and can still increase your rates. Speeding +49km/hr and driving with dirty plate could still be under the "minor category". They don't set different premiums for moving and non-moving convictions; if you're charged under the HTA, it's all the same.
Companies like State Farm will cancel your policy if you collect 3 minor convictions within the same window. Major and Serious convictions will generally result in your policy getting cancelled or +100% surcharges so that you will cancel.
If your charge is related to a sign, there's a small chance they could amend it to the by-law for the sign. It never hurts to ask, but you will not get an amendment to a completely unrelated charge.