名詞辞書形（できるものがある）Can't be out of the present tense. な形容詞（残念なものがある） い形容詞（すごいものがある）
I'd also say the definition could be something along the lines of "shows strong emotions/feelings of the speaker about a fact or a characteristic of something/someone." "Has the feeling of ..." This one is a bit hard to get down. という感じがある and ように感じる are a couple definitions I see but they are hard to really translate.
Well, I updated the usages and appended the meaning. I'm not sure the speaker is always going to have that emotional/feeling connection, though. Here's an example out of a book in front of me:
この映画には人の心に響くものがある.
This doesn't seem to suggest anything about the speaker - they're just stating a special fact about a particular movie and how it affects other people.
Alright, I had a bit of a chat with a native in regards to this. It's definitely a tricky one.
You were half-right about that it brings forth some kind of emotion or feeling, but it's not restricted to the speaker (which is how the sentence I stuck in there 2 posts above works).
Although I didn't understand this part 100%, she emphasized that the feeling/emotion is not something that can be concretely explained by the speaker - it's got a sense of vagueness to it. I'm not going to add that to the definition because I'm not exactly sure on it, but I thought it was worth mentioning.
PS: check your sentence submission for this grammar, I'm about to add some comments she had on it.
