Your sentences are a perfect example! The first one has a subject, “I,” and a verb phrase, “have noticed.” (It’s also got a “subordinate clause” with a subject and verb: “that sentence fragments are hard.”) All together, the sentence is complete by itself. “I have noticed that sentence fragments are hard.” That makes complete sense by itself. It could have been the whole comment.

Now, listen to the other sentence, by itself: “Probably the hardest and not very easy to spot.” If I say it by itself, it leaves you waiting for more. What are the hardest? What’s not very easy to spot? The reason it leaves you with questions is because there’s no subject. (There’s no verb, either. This sentence is really just full of adjectives, so it’s meant to describe something. But all by itself, it’s got nothing to describe.)

So, what’s the best way to fix the problem?