Modal Dialogs and Accessibility
Modal Dialogs are seen to be problematic for both touch screens and accessibility concerns. The issues include the focus of the dialog.
Dialogs can also be non-modal where it is possible to intereact with the dialog content from outside the dialog.
There seems to be a difference in the understanding between "modal", "non-modal" and "modeless". However, this doesn't really matter as a designer of a User Interface the result of what you code is what matters.
The "modality", in my estimation, is that the display interupts the flow of an operation. A "non-modal" or "modeless" does not. In the discussion of Modals it seems that the description is about "non-modal" or "modeless" displays.
Alert Box Dialog
Using an Alert Box for presenting information to the user can be problematic.
By my definition the Alert() is a modal as it needs to be dismissed before the user can proceed.
An alert with a time-out would minimise user disruption.