Sounds like there's more than one problem with the plane. They're never much cop straight out of the box unless you shell out for a Lie Nielsen, but you can get a Record to produce amazing results with some work - at college we spent 4 days tuning our jack planes, so see if you can find some Youtube tutorials. I'd recommend getting a 560 x 230mm piece of 8 or 10mm float glass, spraymount two sheets of 80 grit wet & dry on it and you'll have a means of getting the sole, frog, plane iron etc. dead flat, then you can progress through fine tuning.