This is a notorious and well-known issue in SharePoint.
Let me explain why it happens: SharePoint is a Microsoft product, as is Internet Explorer, and it's quite a customary thing when some features work in IE but don't work in other browsers. Other browsers always were and still are "partially supported" by SharePoint.
This is what happens here: when number of items in a lookup field dropdown exceeds 20, SharePoint transforms a usual dropdown browser control to an advanced dropdown with filtering ability. So if you start typing into this "State" dropdown in IE, it will filter the items as you type, which is in fact quite nice if you have really lots of them.
The simplest solution would be to put some fields after this "State" field (I think even one field will be enough). In this case, there will be enough place to the bottom of the form so the issue will never happen.
Using SPServices is quite simple. You will need to add a Content Editor WebPart to your page, add reference to SPServices.js, and then also embed the following JS code:
For more information, please visit SPServices CodePlex site using the links above, the project is well documented.