I was going to do this as a comment, but I need more characters.
First, the scale. (I'm curious, how does a scale measure height by itself?) Electronic scales can be off by up to 10 lbs in either direction (or more). Mine at home weighs me 3 lbs lighter than a doctor type scale (With the bars and sliding weights). So, if your weight is off, then your BMI is off as well. Where did you plug in numbers to get your BMR, by the way?
Also, most scales that measure body fat do so by electrical impedance (Passing very low current through your body and measuring current loss, which translates into free water, which is used to calculate body fat. (More or less, that's a simple explanation). It can be affected by wet skin, drinking less water in a day, many factors, and can be off by as much as 10% +/-. DEXA is the gold standard, or a 9 spot caliper test done by an experienced tester.
Second - What Nathan is getting at, is that myfitnesspal may say "Sainsbury pink cripps apple, Medium" and give you a calorie count, but that may not translate to YOUR pink cripps apple. The one on MFP might be assigned a weight of 8 ounces, and your apple is actually 11 ounces. There's three extra ounces of apple, and extra calories that you aren't counting.
What you need to do is literally weigh and write down EVERYTHING that you eat for 3-5 days. If you nab an oreo from a friend, write it down. 8 oz of water? Write it down. Eating an apple? Cut it up, weigh the parts you are going to eat, and write it down. That's the only way you will get close to an accurate count. Also, be cautious, many labels give calorie counts per serving, but if you eat the whole package, you've actually eaten 2 or 3 servings (or more).
Here's how it adds up. Say you are in perfect balance, neither gaining nor losing. Starting tomorrow, you change nothing but you eat one serving of oreos a day. 3 cookies, 210 calories. You will gain a little over 3 lbs a year from those 3 oreos a day.
Also, find an actual, calibrated doctors type scale (Many gyms have them), and see if you can get a GOOD bodyfat measurement done.
Once you've done all that, you'll be in a much better position to estimate where you are, and what you need to do to either gain or lose weight. Right now, you're basically throwing darts blindfolded.