Why some corners aren't sticked well?
You can clearly print but there are also some problems it seems.

To see if you're about okay when it comes to leveling, I recommend to activate the 'skirt' in your slicer soft. Slic3r has it and I think most others too, it just makes the printer do a big one-layer all-around 'perimeter' around what is going to be printed before starting. You'll see quickly if there is not enough or too much space between the bed and the nozzle. You might catch other problems too (I love it because when the hotend drips a bit when leveling it get's smeared out far away from where the print is going to happen). 

Your print looks like it is not optimal (overextrusion? no print-cooling? ...) so start with slowing down, first layer 20-25mm/s (Look at it when it's printed, it's very telling!). Then for the following ones, don't go over 40-50mm/s for starters.

Last but not least, you are printing ABS (but you said you had the problem with PLA too, hence my post), I have never printed ABS but for what I have read, you'll need a heatbed and a heated chamber(enclosed printer) to not have this kind of problems.

But for PLA especially; If you have a heat bed, don't put on too much heat when printing, I went from 60°C to 50°C, first layer, 30° then, and my prints now stick like they are melded onto my plate instead of skidding around.