UPDATE:
I found in the bootstrap.min.css, the following entry:
select,textarea,input[type="text"],input[type="password"],input[type="datetime"],input[type="datetime-local"],input[type="date"],input[type="month"],input[type="time"],input[type="week"],input[type="number"],input[type="email"],input[type="url"],input[type="search"],input[type="tel"],input[type="color"],.uneditable-input{display:inline-block;height:20px;padding:4px 6px;margin-bottom:10px;font-size:14px;line-height:20px;color:#555;vertical-align:middle;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;}
if I remove -moz-border-radius:4px;
the problem is resolved.
Any ideas why, given that I thought IE8 ignored that anyway?