They could just have an “ad” screen like the about screen. Encourage users to check it out or leave it open for a time as a source of support for the product.
I’m guessing the most innocuous is just a banner ad of reasonable size that doesn’t detract too much from usable space.
Or, you know, people could pay for their software.
I think I bought a ton of shareware that had innocuous purchase ads (eg, id’s commander keen). The idea isn’t that ads are bad, but that having continuous ads over and over is annoying and unlikely to result in me buying.
