I agree with Dave Nealon. The plural form covers the singular meaning because it's used as a class. For example, we say "one or more objects" to mean "one object or several objects". We read this quite naturally and have no problem with the lack of agreement in number implied by "one objects". As Dave points out, the plural doesn't preclude zero or one of the objects.
I find "one or more object(s)" to be much harder to read, as I have to parse the phrase with both possibilities. The parentheses are a distraction. As 'coleopterist' points out, the Chicago Manual of Style recommends against using it unless it is simple and effective. I would argue that it isn't simple enough, and using the plural is more effective.
Use of (s) might be necessary in legal documents, which have to be very precise and cover all the possible meanings. In ordinary writing, in graphical interfaces, and in technical documentation, I don't think it's necessary at all. I suspect that programmers want to be more precise than is necessary when they use this form in graphical interfaces. As a technical writer, I've always used the plural, and recommended it in our graphical interfaces.