I definitely found one problem (easily fixed). The mono library isn't being tagged at all. Fixing this won't effect Unity specific symbols though.
Under the covers, SlickEdit is automatically building and extension/language specific tag file for you. UnityEngine.dll and UnityEditor.dll are the only DLL's being added to the tag file. Go to Tools>"Tag Files...". Under "C#" tag files you will see the unity.vtg tag file with these two DLL's listed. SlickEdit can read symbols out of C# DLLs just like it can parse symbols from source files.
Use the "Symbols" tool window to browse the symbols in the "unity.vtg" tag file. If a symbol is not present, it won't be possible for SlickEdit to auto complete that symbol.
Using the Symbols tool window, I couldn't find any classes specifically named UnityEngine.UI. I did find some classes that are named something like UnityEngine.UIxxxx (like UICharInfo,UILineInfo,UIVertex). The UnityEngine.Canvas class appears to be tagged. You'll need to be more specific about indicating what symbols aren't listed and post some sample source accessing UnityEngine.Canvas. Again, if a member of that class is missing, there's no way auto-complete will list the symbol.