I'm not personally too familiar with this stretch of the Mississippi, but rapids are usually marked on the maps, and their class (from class I to VI) is listed. Of course in high flow the rapids may be worse than listed, so always scout it out if you're not sure. The current water levels from gauges along the river can be viewed here http://dnr.state.mn.us/river_levels/index.html obviously the higher the flow, the more risk.
Take a look at the Mississippi water trails site I mentioned before though.
http://www.dnr.state.mn.us/watertrails/mississippiriver/index.html
Then click on the section you're interested in. Grand Rapids is part of the Vermillion River to Palisades section:
http://www.dnr.state.mn.us/watertrails/mississippiriver/three.html
This page will give you a short description of this stretch of river, and near the bottom will tell you about any rapids present. For this section it says there are no major rapids. It doesn't mean there won't be any, just that they should be below class I, and very minor. I'm not sure how familiar you are with rapid classes, but in a canoe you should be able to handle class I pretty easily, and class II with some experience. Class III is about the limit for open canoes, and you run a risk of swamping the canoe.
But be aware rapids may appear where there were none before if the flow of water is high enough, or may move up a class, from class I to class II for example, so be extra cautious when the flow of water is high.
Also, some of the sections mention swift water currents. These can be as dangerous as rapids if you're not ready for them, as they may quickly steer your craft into a hazard that could capsize you. Make notes of where these sections are so you can be better prepared for them if and when you encounter them. Again, in high flow these sections may become more dangerous. Avoiding paddling during spring thaw is the best way to avoid high flow conditions, but heavy rainfall can be unpredictable. Usually the later in the summer it is, the less likely you'll be to encounter high flows.
Another resource I just thought of is A Falcon Guide: Paddling Minnesota.
http://www.amazon.com/Paddling-Minnesota-Regional-Series/dp/1560446900
If you don't want to buy it you might be able to find it in a library, but in Tennessee I'm not sure if they'll have it. It gives you some more info on the river sections, and explains hazards a little more in depth than the MNDNR website. Looking through it, under NORMAL CONDITIONS Class I is the highest class of rapids you should encounter between Itasca and Iowa.