Wash the canvas using a fabric softener. You can use a large-load washing machine but if the canvas is old, be prepared for a lot of the stitching to come apart. Good quality fabric, like Sunbrella, lasts an amazingly long time if it's kept clean. Accumulated dirt, mildew, mold, etc. will gradually destroy the fabric itself.
But the main reason fabric covers fail is not the fabric but the thread. The thread rots or deteriortes from UV (or both) and when it lets go the canvas can start beating itself apart.
Some of the Sunbrella covers on our boat were ancient when we bought the boat, particularly the large, two-piece cover for the entire flying bridge. We figured we'd be lucky if it lasted a year or two, given our frequent winter storms that can have gusts up to 70 mph or more. Twelve years later, we're still amazed at its longevity. The fabric, that is. Not the thread.
The only reason we have not had to shell out thousands of dollars for new covers (yet) is because of my wife's dilligence in repairing or replacing any seams that start to come apart. The secret to long-lived seams is the thread and there is only one thread on the planet worth using on boat canvas. That is Tenara from Gore. This stuff is pretty amazing--- impervious to UV, salt, dirt, algae, mold, mildew, heat, cold, chemicals, you name it. It is also amazingly expensive. While you can find it online for lower prices, when we bought the spool that my wife is still using, the lowest price I could find online was about $150 or so. Most places had prices ranging from there up to $300 and more for the same size spool. But it's worth it given the expense of replacing canvas.
So having the seams come apart in the wash is not necessarily a bad thing because it tells you they were about to come apart on their own anyway, and now you can re-sew the seam with Tenara (or whatever you want to use) and greatly extend the life of the cover.
One way to reduce the chances of not having an old seam come apart is to not wash the fabric in a machine. Use a garbage can with whatever detergent and fabric softener you want to use and wash the fabric by hand. Or stir it with a broom handle. Whatever, but it will be less stress on the seams than a machine.
Scraping the accumulated crusty dirt off will most likey result in your weakening the fabric underneath, so better you wash it instead.
There are ways to treat Sunbrella (and I assume other kinds of boat canvas) to minimize the accumulation of new algae and mold and provide a degree of waterproofing to. It involves using at least one additive in the wash as well as 303 fabric protector afterward. My wife has the "formula" and the application process down pat--- she was instructed in it by the local shop where she gets her Sunbrella--- but I don't have a clue what it is. It works really well, however, as on things like the flying bridge surrounds where we were constantly getting green algae or mold growth during the winter we no longer do. I suspect you can find the information on-line. Sunbrella itself may have a recommendation on how to best care for their fabric on their website. It's not a permanent protection, however. Nothing is in the weather a boat lives in. It's something you have to do periodically depending on the climate and weather in your area. More of a problem up here in the PNW, I suspect, than in California.