Hey,
I tend to remove this as well sometimes when I develop custom sites.
One way to do it is to edit: http://yorsite.com/wp-admin/css/colors-fresh.css
Find #update-nag and update it to the following:
#update-nag {
background-color:#FFFEEB;
border-color:#CCCCCC;
color:#555555;
display:none;
}
for the plugins, look for: .plugin-update-tr .update-message and update to:
.plugin-update-tr .update-message {
background-color:#FFFBE4;
border-color:#DFDFDF;
display:none;
}
This will remove the yellow "update plugins" row, but you'll still see the count of how many plugins needs to be updated (and the list of "upgrades available") without the means to "upgrade automatically"
...Also, you can disable the "upgrade automatically" option and display a custom message:
http://dd32.id.au/2009/01/29/disable-automatic-upgrades-for-a-customised-plugin/
Cheers,
Q