Something that doesn't appear to be mentioned in here that bit me recently is that views follow a table through renames. Ended up having views that were subtly broken because they were pointing to the tables that I had renamed to have an _old suffix instead of the newly created ones I had expected them to point to.
This is a very good example of why you should be using a schema diff/comparison tool.
Run your rename on a copy of your production schema, then run a diff tool to see what's actually changed - in this case it would show a view definition had changed and even autogenerate the replace statement you would need to add to fix the script.
What specific tools would you recommend for schema diffs?