After you get to the save file dialog in most browsers, your download has already started while you type in a file name. After you click save, a significant amount of data has already been downloaded and the "meter" if you will, has to catch up so the measurements will be higher for a few seconds then slow down to normal.
As for uploads, I suppose a similar method is taking place. Data is probably being accumulated before a connection is fully negotiated, that's why it seems to be a "burst" at first. Although I've never had this happen to me with uploads, probably because I don't upload enough to notice. Both of these oddities are not specific to dial-up though.