I had exactly the same problem when migrating from bootstrapv2 to v3.
If (like me) you migrated by replacing the old spanX with col-sm-X you also need to add col-X classes. col-X are the styles that are outside of any @media blocks so they work without media query support.
To fix the container width you can set it yourself outside of a @media block. Something like:
.container {
max-width: @container-tablet;
}
@import "twitter-bootstrap/less/bootstrap";