I had similar problems. I’ll describe the problems here, and then my solutions:
Problem 1) The Links section in my sidebar didn’t display properly, but instead there was an SQL error message, similar to the ones listed above
Problem 2) No categories were appearing in the sidebar under the “Categories” heading, even though the category name WAS appearing next to each of my posts
–Solutions–
Solution 1) Edited sidebar.php, taking out get_grouped_links_list and replacing it with wp_list_bookmarks. You might not have “get_grouped_links_list” (I believe it might be exclusive to the theme I use), but you probably have “get_links_list”, which is now deprecated and should be replaced by “wp_list_bookmarks” if you’re having issues.
Solution 2)Edited sidebar.php, taking out category_cloud and replacing it with wp_list_categories. You probably won’t have the “category_cloud” function in your sidebar unless you are using the “durable” theme, but you might have another category function that doesn’t work with wp 2.1, and which you need to replace with “wp_list_categories”.
Hope this helps someone