Fixing these small mistakes can improve your guitar playing dramatically.

Teaching yourself to play the guitar can be a little dangerous, because without that extra set of trained eyes a teacher has, you can miss some small fixes that make a huge difference in your playing.  Here's three very common mistakes that are easy to fix.

Easy Fix #1: Holding your pick correctly.  Incorrectly gripping your pick will only get you a floppy, slapping sound and a lack of control.  You may see some different techniques out there, but I've found this one to be very comfortable for beginners.

Hold the pick between the pad of your thumb and the side (not tip or pad, but side) of your index finger.  Your thumb covers most of the wide part of the pick and your index finger covers the back part.  Only about a quarter inch of the tip of the pick should stick out.  More than that gives you that slappy sound you don't want.

With experience you'll learn to adjust your pick for different situation.  When I'm playing a single note melody I use even less than that quarter inch.  Just the tiniest tip.  For strumming I'll use a little bit more pick.

Hold the pick just tight enough to keep good control of it while you strum, but not so tight that your hand is stiff.  If your hand gets sore, you're probably holding it too tight.

If you're having trouble picturing how to hold the pick, Dunlop makes a line of training picks that have grips in the right places to teach you how to hold it.

Easy Fix #2: Your picking direction.  Which direction your pick is going affects how your strum will sound. That's why sometimes you'll be playing the right rhythm, yet something sounds off about your strum.  There are exceptions to all of these, but these guidelines will always get you in the right place. 

When strumming quarter notes: 1  2  3  4
Use all downstrokes.

When strumming eighth notes: 1 & 2 & 3 & 4 &
Alternate starting with a downstroke on 1.  Each down beat (the numbers) will be a downstroke.  All the "ands" will be upstrokes.

Possible Exception: In metal and hard rock music, eighth notes are often all downstrokes because it makes them sound more aggressive.  You'll switch to double stroke picking for 16th notes and faster.

When playing sixteenth notes: 1 e & a 2 e & a 3 e & a 4 e & a
You'll play these with alternate picking as well.  This time the downstroke with be on the 1 and &.  the upstroke will be on e and a.  The main difference here, from eighth notes, is that the "&" gets a downstroke instead of up.

If you have a rhythm that leaves out note such as 1 _ &  a, you will still stick to the normal picking pattern.  Down on “1”, down on “&”, up on “a”. 

Always keep your right hand moving in an up/down motion the whole time, even if you're not hitting anything on a particular beat.  That creates your own metronome and your strumming and rhythms will sound more connected.

Easy Fix #3: Left thumb placement.  This can be a hard habit to break if you've developed a bad one, but you'll thank me when you get correct.  The thumb on your fretting hand should be in the back of the neck, roughly pointed towards the ceiling.  Don't flop it over the top of the fretboard.  If someone standing and facing you can see your thumb, it's too high.

Having your thumb in the right place you'll expand your stretch a lot.  This will also help you use the right muscles in your hand.  You'll use the large, strong ones near your thumb rather than the smaller, weaker ones just below your fingers.  You always want to fret the note by squeezing it between your finger and thumb, as if you were squishing a particularly loathsome grape.

Possible Exception:  There's two times your thumb can come over the top.  When you're bending notes, bringing your thumb over the top gives you a bit better leverage.  There are also Jimi Hendrix style chord forms where your thumb will hold down the root of the chord on the bottom string while your other fingers grab the rest of the chord.  It's unorthodox, but works very well for some of his lines.

Make a conscious effort to fix these three problems in your playing and I know you'll see a lot of improvement in your playing quickly.