1. When you say "WebDirect on FileMaker Cloud Can't edit records" (in title), I'm assuming that Cloud is the only place where you host files for WebDirect access? (and not that you also have FileMaker Server running on an on-premise machine and you can edit these records fine in WebDirect there). Just to determine if this specific to Cloud hosting, or a WebDirect issue in general.
2. Do you happen to have a copy of FileMaker Pro 15 to try editing these records with, and if so, does that work fine? FileMaker Cloud is still running essentially a FileMaker Server 15 code base, so any features or options that are new to FM 16 would not display in a WebDirect client there (though they might in a 16 Pro or Go client).
3. When you say "users are unable to edit records," what specifically do you mean? They can't click into fields? They can click in, but can't make changes? They can click in and make changes, but their changes aren't saved?
4. If they can't even click into fields, is it possible those fields are covered by transparent objects on that layout? (e.g. see this other current thread: Re: Webdirect field uneditable, but fields on iOS and Mac clients can be edited)