Suppose my Azure role stores files to the role local filesystem and forgets to delete them. Can another application that uses that host in future possibly get access to those fi
Although I am not sure it's properly documented, I am fairly certain that Windows Azure recycles thoroughly whatever local files haven been dumped by a Role into a VM before letting any other Role access the VM. That's a fairly basic security policy.
Then, considering the deployment time on Windows Azure for a new VM (between 6min to 8min) I am pretty sure that the VM itself is pretty much wiped-out clean, not just the local storage, so that whatever by-product files which might have been generated by the OS itself during the execution of the VM does not become available afterward.