"The moon is more closer to the earth than the sun". Are there any issues grammatic wise in this sentence?

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This is a general grammatical rule, if you are describing something with an adjective that ends in -er you can not put the word "more" in front of it. For example you could say "it is more bright outside than inside" OR "it is brightER outside than it is inside" but NOT "it is more brighter outside than inside"

Moreover, the same rule applies to adjectives ending in -st.

"This is the most clean I've ever seen this place" OR "this is the cleanest I've ever seen this place" but NOT "this is the most cleanest I've ever seen this place"

There are some adjectives than will only make sense one way however, so when you stumble across them, just keep them in mind! Hope this helps!