While any Android device can be programmed, there are some caveats you should be aware of.
First, what features are available to you as a developer depend very much on what version of Android is installed on your tablet. Very importantly, a tablet that is running a version of Android below 3.0 Honeycomb (or ideally 4.0 Ice Cream Sandwich) will not have any of Android's tablet-specific features accessible to it.
Second, an app you develop will not necessarily run on all Android devices (or even all Android tablets). Obviously tablets that run a version of Android lower than what you have targeted with your app won't run it (though there are ways to make such apps run with some features missing). But also, Android device manufacturers often add a layer on top of Android (for example, Samsung adds a layer called TouchWiz and HTC adds Sense). If your app uses any of these added features, it won't run on devices that don't have it.
Lastly, I don't know where you are, but in India, where I live, there are a ton of cheap unlicensed Android tablets. If you buy one of these, all bets are off, since these manufacturers have not committed to rigourously testing their devices for full compatibility, which is one of the conditions required to be an Android licensee. In general, stuff will probably work on these tablets (provided the above criteria are met), but you can't count on it. Since these tablets don't have access to the Google Play store, so you're going to have to sideload any apps you install on them.
Despite these exceptions, the majority of applications will run flawlessly on most Android devices. The Android development tools are pretty good at warning you about API incompatibilities and it's pretty difficult to accidentally use a device/manufacturer specific API.