What was your shutter speed?
the rule of thumb is to use a shutter speed of 1/focal length to avoid camera shake so at 300mm you should be at 1/300th sec or fasterI . It gets a bit more complicated as you also need a shutter speed fast enough to freeze motion. Just exactly how fast you need depends on the bird and what they are doing. For perched birds 1/300th sec should be ok, for large birds in steady flight 1/800th is normally fast enough, if they are activley changing direction then 1/1000th sec or more. I was shooting sparrows and starlings yesterday and had to bump the shutter speed right up to 1/4000th sec in an attempt to capture the action.
The shutter speed was 1/500 in both pictures. In both pictures I am looking at the grain in the birdfeeders as well. I have heard people say that certain lenses can have a blur when fully extended. I suspect that this is the case. Today or tomorrow I will go out and conduct an experiment with different focal lengths.
I admire you for being able to capture birds in flight. I have only been birding for about one week. There is so much to learn. I appreciate your advice. Will also try the 1/800 and 1/4000 shutter speeds out of curiosity.
Actually its human induced blur.
A camera lens is essentially a lever for light.
If I remember Mr Radant's freshman college physics class from 47 years ago, doubling the length of a lever ... call it 150 X 2 = 300 for simplicity ... you create 4 times the human induced movement at 300 as you would have at 150.
As an experiment to visualize this, close one eye and leave your dominant eye open, extend your arm and point with your index finger at a fixed object 10 feet away and note how much movement is in your index finger at the tip. Now extend your arm holding a yardstick aimed at the same object and notice how much movement is at the end of the yardstick.
The simplest fix is to increase the shutter speed when possible, and it will also help freeze any motion in the subject matter.
An additional easy fix is to turn on VR if you have it. If not a decent tripod or monopod will do wonders and are plentiful ... and cheap ... used.
The best, and most fulfilling IMHO, solution is to develop decent handholding skills.
Here are some technique tips I have learned over 54 years as a photographer:
1 - With a longer telephoto hold the camera with your right hand, and place your left hand on your right shoulder. This will have your left elbow extended forward, keep it as level as possible and rest the lens in the crook of your elbow. Your elbow can be raised/lowered instinctively/easily for aiming. It may feel a bit odd at first, but becomes intuitive quickly.
With a shorter lens, hold the camera as before and cradle the lens in your left hand. This stance can also be used with a zoom telephoto if you are racking in and out routinely.
DO NOT hold the camera with two hands, one on each side like a tourist with a point and shoot.
DO NOT grip the rig very tightly, muscle tension induces vibration. Rig security is why you use a strap of some sort. Hold it more like you would a baby bird ... enough that it won't get away, and no more.
2 - Stand at a right angle to the subject, make sure your left shoulder points toward the subject. Spread your feet to shoulder width or a bit more. I prefer to point my left foot towards the subject, but this is preference, because it allows me to turn a bit quicker. I also use my weight shifted just a bit onto my forward foot, lets say 60-40.
3 - If you use your left hand as a lens support, tuck both elbows against your body, if you use the left elbow as as a brace then just rest the right elbow against your body. In either case you want to remain loosened not tense.
4 - At the moment you actuate the shutter, briefly pause your breathing or at least breathe as slow and shallow as possible. A half second or so should be plenty.
5 - This is the biggest beginner mistake, and the easiest fix, depress the shutter with the pad of your index finger only.
6 - Place the viewfinder
DO NOT squeeze the camera with your hand. This induces vibration at a horrible level.
I know this sounds like a lot, but developing those skills can get you stability with a 300 down to 1/125 second fairly quickly.
I hope this helps.