This is because your sidebar links are block elements. In your CSS, you have:
#sidebar1 a, #sidebar1 li.recentcomments, #sidebar1 .textwidget, #sidebar2 a, #sidebar2 li.recentcomments, #sidebar2 .textwidget {
border-bottom:1px dotted #000000;
color:#A5A5A5;
display:block;
padding:3px 3px 3px 10px;
}
This tells the browsers that any link in your #sidebar1 or #sidebar2 is a block element. That's fine for your menu (in the right sidebar) where the user can click the menu "button" effect as opposed to only being able to click the menu text, but it is also the reason the twitter links are pushed to the next line. Your CSS is telling the browser that the links should be "block" elements in their own space as opposed to "inline" elements.
Separate the #sidebar1 css from the #sidebar2 css so you can tell the #sidebar2 links to be block elements, but not the #sidebar1 elements. Your CSS might look something like this:
#sidebar1 li.recentcomments, #sidebar1 .textwidget, #sidebar2 a, #sidebar2 li.recentcomments, #sidebar2 .textwidget {
border-bottom:1px dotted #000000;
color:#A5A5A5;
display:block;
padding:3px 3px 3px 10px;
}
(Notice the missing "#sidebar1" from the CSS.)