Using Glue With Animal Plastics Rack?

Hey guys, christmas came early when I saw a huge box labeled "ANIMAL PLASTICS" in my driveway hahah. Its a 3 level high sterilite rack which I have recently unboxed to make sure everything looks right (which is does) I am only 20 and not at all a hefty construction guy so of course my father would be helping and he took a look. He mentioned how the wood used in it was soft and and offered he used some wood glue on it. He said it is called "Liquid Nails" and holds wood together extremely well and would work well. He said it is very heat resistant and would not be toxic once dried so I dont really see a problem, do any of you? I wanted to take to these forums strictly cause snakes are involved, other than that my dad is a scientist so i usually trust him and things like this. Can anyone find a problem?! Thanks in advance :confusd: