If you use any webclips that have a picture of the website as the thumbnail (left from your previous iPhone), re-create them to get the high resolution icon.
Obviously this won't work with websites that provide their own icons and haven't updated to them to high resolution ones, e.g., Sigalert (I've emailed them requesting the high resolution icon).
Obviously this won't work with websites that provide their own icons and haven't updated to them to high resolution ones, e.g., Sigalert (I've emailed them requesting the high resolution icon).