1. In reality, the geological records do not always appear in the nice little multi-layer strata that 'evolution' textbooks present it to be. Some appears to be folded over or upside down. i.e. some supposedly more modern strata appears below that of more ancient ones.
This is Geology 101. In other words, yeah, scientists know that and take it into account when they evaluate fossils. A paleontologists will evaluate the geology of the site as well as the fossils within it. Radiodating of the rocks can tell you the age of a particular layer regardless if it was folded or flipped.
2. There has never been any transitional fossils found (i.e. from fish to amphibian or reptile).
This is a simple lie.
Here are some examples...
http://www.talkorigins.org/faqs/faq-transitional.html
Genetics shows that fish is equally distant from birds as humans and in fact, all other vertebrate animals.
Show me the data.
3. The so-called human ancestor skulls (such as lucy etc) has more paris-plaster than bones and there aren't even enough 'ape-man' bones to fill a proper casket.
It is true that 100% complete fossils are not found and that there are not a lot of human ancestor fossils compared to other species; however, that's about the extent of the truth in this statement.
From Lucy's species alone (A. afarensis), there are over 300 specimens (fossil bones) found from over 111 individuals of that species. We can tell the bones come from different individuals based on (1) their location (2) their repetition (e.g., if you find two mandibles, you know they didn't come from the same individual). Based on the array of specimens/individuals, you can piece together a pretty good complete picture.
Similarly, large numbers of specimens from many individuals were found from other species (e.g., over 500 individual Neandertals have been found, over 100 individuals from A. africanus, ~100 specimens of A. boisei, over 40 specimens of A. ramidus, etc. etc.)
A great summary of this can be found in Donald Johanson's book "From Lucy to Language" (which is my reference for those specimen/individual numbers).
4. The Cambrian explosion. No one can explain how millions of years went by with single cell organisms and suddenly at the cambrian age, a hosts of multi-cellular creatures with sufficient complexity appears out of nowhere.
They didn't appear out of nowhere, but they did appear suddenly (geologically speaking of course) in the fossil record during that time period. However, this is likely a record of new body types that were amenable to being fossilized. Previous mulitcellular lifeforms were likely too soft-tissued to be turned into a fossil.
5. Mutations. Mutations are generally errors in existing genetic codes. Can mutations introduce new genetic code? If mutations occurs in DNA, then the same mutation must exist in RNA to for it to read the DNA and express the right proteins. In other words, fins don't start turning into limbs due to mutation or because fishes start taking a walk on the beach several times a day, but by the introduction of new genetic code. To put it into an analogy, genetic mutation is about the same as a sentence being smeared. It will become blurrer, but it won't turn into a new picture or a new sentence.
Misrepresentation.
First of all, mutations can add new information to the genetic code. A gene that was AAAA that becomes AAAC is something new, although it may be nonsense in any particular instance. It is incorrect to say that every mutation is harmful ("smeared" sentence as stated above). Many mutations are harmful, but some are neutral (no beneficial or adverse affect) and a rare few are beneficial. But mutations are not only point changes (for example, changing a A to a C) but can also include duplications, reordering, and flipping of gene codes. A hypothetical example may include a 10-segmented bug that becomes a 12-segmented bug with a mutation to the gene that regulates the development of body parts. A mutation or two won't turn a sea creature into a land creature, as strawmanned by the example, but mutations (and recombinations, etc.) create a variation in the species population. Some variations may have stronger/flatter/whatever fins compared to the others and that subgroup could find itself in a shallower water zone in which scooting across the seabed would be beneficial. And thus the slow change toward ever-more walking begins. Here, I'm providing a hypothetical example as I don't have a specific example of this on hand, but the idea is the same. The important point is that the transition occurs (1) slowly and (2) within the margins of the current habitat (fish didn't leave water and then develop legs...they developed leg-like appendiges while still in water and then they were able to take advantage of that feature when circumstances changed).