jQueryUI supports the following jQuery version range:
"dependencies": {
"jquery": ">=1.7.0 <4.0.0"
},
I’d say you’re good to go.
Source: https://github.com/jquery/jquery-ui/blob/master/package.json#L49
It might be that you’re seeing a lot of broken components because either you’re not importing their CSS or you’re overriding their CSS.