The query form in the admin UI could use an improvement regarding how the request handler is chosen; presently all there is is a text input for 'qt'. The first choice to make in the form above the query should really be the request handler since it actually handles the request before any other parameters do anything. I think it'd be nice if it was filled with "/select" by default to make it very clear what's there, although I realize most of this query form seems to prefer blank values as defaults. When the form creates the URL to submit to Solr for the search, it needs to do something different depending on wether this value starts with a '/'. If it does, this goes where "/select" goes in the URL normally (i.e. it's the tail end of the path after the core). If it doesn't then it goes into the 'qt' URL parameter.
I did something similar to the old 3x UI in
SOLR-3161 that got committed to 3.6.