Having Problems with stubborn pixels in GIMP.

[Non Nomen]

So I'm new around here, and also not particularly experience in using GIMP to make maps, and I keep running into problems with making this world map for an RPG game I'm trying to run. First time it was crashing everytime I try to apply bump maps (that seems to have creeped in again, when it wasn't being a problem on this iteration of the map earlier) Anyways the specific issue I have is that I've got these sets of pixels that have decided they don't want to co-operate with me today. They stay like this regardless of what color I paint them, whether or not I apply filiters to them, and seem to stay like this even if I make new layers which is particularly annoying. Anwyays I'm wondering if any of you know what on earth is going on with this, and how I can fix it.

[bkh1914]

I'm not sure which pixels you are talking about...
But it looks like you have an active selection for the white area. If that was selected by color, then the selection isn't necessarily binary (on/off). Some pixels might be partially selected based on how much of that color they have and by anti-aliasing / feathering. Those pixels won't respond completely to any operation.
[The marching ants for a selection seem to run at about the 50% selected level. An area that is 51% selected will be inside the boundary, but only 51% of the pixel will be effected by the operation. Conversely an area that is 40% selected won't be inside the boundary but it will still be somewhat affected by an operation.]
If you did a selection by color (magic wand), try using a higher threshold.
Shrinking and then growing the selection (or growing and then shrinking) often eliminates 'rogue' pixels.

I see you've added a layer mask. Same thing applies to a layer with a layer mask. Pixels that are partially masked will only be partially affected in the composite image.

(I've chased those problems more than once.)

Edit: I just noticed that you are doing a bucket fill of similar colors. You might have better luck filling the entire selection.
(I've never used that fill option, and I've been using GIMP for a long time.)

Edit 2: the quick-mask can be helpful for finding stray selected or unselected areas.

[Non Nomen]

I'm not sure which pixels you are talking about...
But it looks like you have an active selection for the white area. If that was selected by color, then the selection isn't necessarily binary (on/off). Some pixels might be partially selected based on how much of that color they have and by anti-aliasing / feathering. Those pixels won't respond completely to any operation.
[The marching ants for a selection seem to run at about the 50% selected level. An area that is 51% selected will be inside the boundary, but only 51% of the pixel will be effected by the operation. Conversely an area that is 40% selected won't be inside the boundary but it will still be somewhat affected by an operation.]
If you did a selection by color (magic wand), try using a higher threshold.
Shrinking and then growing the selection (or growing and then shrinking) often eliminates 'rogue' pixels.

I see you've added a layer mask. Same thing applies to a layer with a layer mask. Pixels that are partially masked will only be partially affected in the composite image.

(I've chased those problems more than once.)

I'm mostly talking about those rings of partially invisible pixels near where the mountains are, those are very much within my selection area and for whatever reason they don't want to take up the same colors as the pixels around them. This is also a problem when I try to apply gradient mapping, and noise filters. I also seem to have the problem in other selected areas, and I'm not sure why it is happening.

[bkh1914]

I'm mostly talking about those rings of partially invisible pixels near where the mountains are, those are very much within my selection area and for whatever reason they don't want to take up the same colors as the pixels around them. This is also a problem when I try to apply gradient mapping, and noise filters. I also seem to have the problem in other selected areas, and I'm not sure why it is happening.

My suspicion is that either the layer's pixels are locked or that it's alpha channel is locked.
In the layer tab, with that layer selected, look at the frame at the top of the layer list. There are two small icons to the right of the word 'Lock:'. The brush one locks the pixels for that layer and the painting tools won't do anything (brushes, fill, etc). The other box locks the alpha channel - you can change colors but can't change the opacity. Each icon will have a little black border around it when it is active. Make sure that both of them are inactive (no solid lines around them).
[The icons reflect the status of the currently selected layer.]

[Non Nomen]

My suspicion is that either the layer's pixels are locked or that it's alpha channel is locked.
In the layer tab, with that layer selected, look at the frame at the top of the layer list. There are two small icons to the right of the word 'Lock:'. The brush one locks the pixels for that layer and the painting tools won't do anything (brushes, fill, etc). The other box locks the alpha channel - you can change colors but can't change the opacity. Each icon will have a little black border around it when it is active. Make sure that both of them are inactive (no solid lines around them).
[The icons reflect the status of the currently selected layer.]

So I managed to figure out what the problem was. It seems that your original suspicions about the pixels being only partially selected were correct, although I'm not sure why it was working that way as I had been using a selection from path when that happened as I remember. I only realized what the actual issue was when I started trying to work on another section, and ended up changing pixels in areas completely outside of my actual selection area which I solved by de-selecting them with the free select tool.