The CanIt web interface is designed with Web Standards in mind, so the interface should work fine on any device. That being said, there are some considerations to keep in mind while using mobile devices.
Some mobile devices will automatically capitalize the first letter in any given text field. This includes both the login field and the Change Streams field. The trouble with this is that CanIt streams are case-sensitive and so logging in or changing streams with a misplaced capital will land you in a stream that does not exist.
How to avoid this behaviour
Admins can change the Setup->User Lookups entry that they are using for authentication to have the "Force user name to lower-case?" parameter turned on. This will allow users to log in with any combination of capital and lower-case letters. This will, however not help with changing streams, but that is only a concern for the admin users themselves.
iOS also allows you to turn off auto-capitalization. The setting at the time of writing (in iOS 9) is Settings->General->Keyboard->Auto-Capitalization.Alternatively, if you don't want to disable this feature, you should be able to add a one letter prefix, type the rest of the name, then scroll back and delete the initially capitalized first letter. This is somewhat tedious, but unfortunately we have no way to override the behaviour of these devices.
Android's default keyboard (Gboard) is much less aggressive about this (true as of Android 7.1), in that it automatically presses the Shift button but it will not "correct" a leading lowercase letter if you specifically disable the shift before typing. Android's keyboard preferences may also be configurable depending on which keyboard you are using. The location of these preferences in version 7 is Settings->Languages & Input->Virtual Keyboard->[Keyboard Name].
Small Screen Size
The CanIt WebUI does offer a simplified UI for mobile devices. This layout only kicks in automatically at very low resolutions, not based on the actual device type, so it is likely that a modern phone will default to the "standard" view. The mobile layout is also only available for two of the base themes: RP-Web (the default on Hosted CanIt) and Iceberg (the newest theme). If you are using one of these themes there should be a box at the bottom labelled "View" that you can use to switch to "Mobile". If you are not using one of these themes, you will first have to switch to one of them using the "Theme" box that is also at the bottom.
It is possible that you will not see either of these boxes because they have been hidden by theme customizations made by your admin. This is sometimes done because customizations are specific to the base theme being used and changing to a non-default theme may remove branding or other changes.