Use more HTML5 input types
We only use type="number" for now.
I think it would make sense to use types email, url and tel as they fallback without problem to a text input and will provide a better interface on some browsers.
We should also use type=search for search fields (may improve experience on phones).
The hard decision is whether to replace our date input by the type=date HTML5 input. Here is the support matrix: https://developer.mozilla.org/en-US/docs/Web/HTML/Element/input/date#Browser_compatibility
All major browsers seem to support it, and I expect most of them will have a better interface than our old fashion datepicker. It would mean switching from d.m.Y to YYYY-MM-DD format for POST value. We may keep d.m.Y as internal value to avoid confusing webservice and internal code (but I do think YYYY-MM-DD is a better and more widely used format).
inputs are using types text, select, url, button and number
Use email, tel, search, date types.