>We've been working on a vertical app.
>
>We're really close on being finished with it. Here's the thing. We saw a demo of a product offered by a competitor.
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>There's a thing that our application has that our competitors does'nt fully offer.
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>But that particular competitor (the demo we saw) says in his publicity that their application is offering it. and in fact it's something that is not really completed yet.
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>
>So from that publicity here's what I understand.
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>. That competitor realized that this characteristic could become very important in the future.
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>. They probably intend to make their software support what they say as fast as they can but they're not there so far so they just fake it in their publicity.
>
>
>How should we react to their (could we say false) publicity?

One thing you must NOT say, publicly or privately, is that your competitor's product does not have the feature. You are not an expert on their product, and you have no idea of how close they are to offering a complete version of the feature.

What you can say is something like:

"To the best of our knowledge ours is the first, and only product with a complete implementation of Feature X. Feature X was introduced in [Version N.N] [Some Month/Year] and has been proven in real-world use at various end-user sites."

Don't bad-mouth your competition. Vertical markets tend to be small worlds where everyone knows everyone else, and people have long memories. Today's competitor may become tomorrow's ally, or boss.

Another approach would be to get both your product and your competitor's reviewed by a third party. If there is a magazine that is the "bible" for your industry that would be a good choice. It looks good if VerticalIndustryMagazine rates your product at 8.9 and your competitor's at 7.2. Failing that, having a review of just your product can be very useful as well - most mags will let you order reprints of just the review that you can use for marketing purposes. I believe there are also reputable, professional software reviewers who can be commissioned to test your product.