Primordial soup/primordial ooze/primeval soup/whatever is a collection of biological molecules in some medium (eg. water) that if assembled correctly, could form some sort of pre-life.

The primordial soup model for the origin of life involves at least one of these primordial soups existing some time in the distant past. One of these soups would develop, through random interactions, the precursor to life as we know it. This could have been RNA (The RNA world model), or perhaps replicating proteins, or maybe something altogether wacky.

There are probably two big issues involved here (besides whether there actually was such a primordial soup):

  • What caused this primordial soup to come about?

    Some experiments have been done to show that under certain conditions that may have been present on the early Earth, certain simple amino acids can be created. Did these conditions really exist? What about other amino acids?

    Some have suggested that the ingredients could have been deposited by comets and other space objects. How many of these pre-biotic rocks are out there? Can the ingredients survive long enough in a space environment? Why do the comets have these ingredients but not Earth?

    There are probably lots of other hypothetical sources, but none come to mind.

  • Does the primordial soup do a good job at making the pre-life?

    Obviously it's just improbable to just mash together some random atoms and get out even some of the simplest life we see today -- even doing it for a billion years with a gigantic soup. Cells may be small, but they are complex.

    That said, there is probably a pathway from some simpler form of life. For example, you probably don't need a cell membrane, or a hormonal system. What is that minimal self-replicating kernel made of? Stability problems with life molecules would seem to require that it has to be entirely generated in a short time.

Of course, you can always say "infinite universe therefore everything happens", but this does not mean that this particular model was the way for us. There could be vastly more probable ways for life to arise, and those would be a better theories.