At first glance, I can spot some suspicious solder joints (red), and a few probable shorts (green). I circled only a few exemples.
I wonder if you iron isn't a bit too hot. Is it around 400°C ? That's how I would explain the brownish stains around each pads. You are probably overheating the pcb, and burning the pcb's flux coating.
I would reflow all suspicious pads, so that the pad is filled with solder : not too little or too much, just enough. Your iron needs to touch and heat simultaneously the component's leg and the pad for 1 or 2 seconds, then you can put a little bit of solder to fill the pad.
Next, clean the tiny spaces between pads, moving quickly with your iron to avoid overheating the pcb. Remove all heat-sensitive components, such as transistors and IC. An old dry toothbrush can be useful to clean the board from all remaining solder bits.
With your digital multimeter (DMM) set on continuity test, following the schematics, you can make sure there is no connection between components that aren't supposed to be connected (shorts). Power supply unplugged and circuit unpowered, switched off.
