If the "green button" you mention is the one (and only one) that I know of then that only appears in the "task" window that appears during the downloading process. It indicates if each stage of the download and install process was successful. Red indicates an error, yellow indicates a warning.
If an asset has been downloaded but not yet installed (for example, if it is open for editing which can occur if the asset is already installed) then it will not appear in the Today filter.
The only options that I can suggest are ones that you have already tried - the Open for Editing filter and the Faulty filter. The fact that it has been downloaded and does not appear in the Today filter, or the other two filters, is quite puzzling. Can you identify the name, <kuid> code of the loco and the address of the web site?