In iOS, Office 365 Web-based editor says you can edit PowerPoints, but you can't insert, edit, or select text. Nor can you import graphics, though you can insert SmartArt shapes -- but not manipulate them. You can add and delete slides. Text selection is similarly unavailable for Word documents, making them uneditable on iOS as well.
In Android 3.1 (on a Samsung Galaxy Tab 10.1 tablet), Office 365 suffers from myriad screen display issues, likely due to a flaw in Android 3.1 given issues I've had on other websites with Android. For example, selection boxes appear nowhere near what you tap, and when editing text in a PowerPoint file, scrolling is disabled when the onscreen keyboard is visible. Text formatting doesn't work, even though the controls are accessible. For Word files, I could not select text, and the browser eventually froze after repeated attempts -- an issue I've also had on other websites. If you do brave Office 365 editing on an Android tablet, be sure to long-tap the file links; otherwise, the Android browser downloads the files.
In Android 2.2 (on a Google Nexus One smartphone), you can edit Word documents in the browser; you can also view, but not edit PowerPoint documents.
In BlackBerry OS 6, you likewise can edit Word documents in the browser and view -- not edit -- PowerPoint documents. (Be warned that a BlackBerry Torch -- RIM's only modern smartphone -- is excruciatingly slow, even over Wi-Fi, and not realistically a device you can use for Web-based editing, whether on Office 365 or any website. This once-promising device now is downright dowdy compared to competitors' current offerings.)
In Chrome OS, you can also edit Word files and only view PowerPoint documents.
You can edit Word files in Firefox and Chrome on Mac OS X, Windows, and Linux and in Safari on Mac OS X and Windows. You can also do a fair amount of editing for PowerPoint files in these browser. (Note: On Safari, I kept getting error messages saying the SharePoint WebKit plug-in could not be loaded.)
Thus, it's clear that the ability to edit Office documents in Office 365 via the Web is highly limited in a mobile environment. In the case of Android, that seems to be as much as Google's fault as Microsoft's. For the rest, I have no doubt that limitations in the WebKit browsers they all use play a part, but Microsoft's reliance on proprietary Web technologies, as well as my early conversations with some members of the Office 365 design team (who admitted they weren't concerned with non-Microsoft environments), suggest that Microsoft didn't even try.
On desktop OSes beyond Windows, you lose the ability to edit the documents in place via a local copy of Office, but you can at least download the files to a compatible editor and upload the revised versions.
Editing files via native apps
As the point of comparison, you can edit documents stored in Office 365's SharePoint using Office Professional Plus 2010, the downloadable suite that comes with midlevel and higher tiers of Ofice 365 subscriptions. You can also use the regular edition of Office 2010 if you download the Office 365 from Microsoft's Office 365 site, as well as the severely crippled Office apps that come with Windows Phone 7.
Because Office 365 is tied to Windows Office for application-based editing, you can't open files in SharePoint in any Office-compatible app on any non-Microsoft operating system -- not even in Office 2011 for Mac, which Microsoft has not Office 365-enabled (par for the course in this perennially crippled product).
In iOS, you can preview a document, then open it in a native application such as Quickoffice, Documents to Go, or iWork for further ediiting, but you can't then send the changed document back to the SharePoint collaboration site, not even from a compatible application (as iOS has no common document store) -- which means you can't collaborate.