Here we go. Steps to making your map better:

1) Do you have the console? If not, edit your Half-life shortcut by right-clicking on it and hitting "properties", then go to the Target box on the Shortcut tab. Add "-dev -console" to the end if it's not already there.

2) Start up this shortcut. Load up your map (try clicking the shiny new Console button at the top and typing "map (mapname)". Look around a bit, see what you like.

3) Now: hit tilde (the ~ key at the top left) and the console box will drop down. Type r_speeds 1 and press enter. You should see a bunch of lines suddenly fill up your console and appear on your screen. The number you are looking at is the one in front of the "wpoly". This is the most important r_speed number. If that ever goes above 800, you start getting those "short xxx faces" errors and the game stops drawing parts of your map, which is bad.

4) The name of the game is "keep r_speeds low". While it probably doesn't matter for your first few maps, in the long run you really want to keep this in mind because the higher the r_speeds, the longer the view takes to render, so it lowers your framerate (and when you play in software mode, stuff disappears!) A good number to keep r_speeds below is 700, though you can probably get away with as high as 1000 in areas not usually travelled, or areas where most people will NOT be fighting.

5) How to lower r_speeds? There are several ways to do this. First, make sure the game isn't drawing too much. A start is to compile your maps with a full vis (open up Hammer's compile window, make sure you're in Expert mode, click on the left pane that says $vis_exe (something) and in the right pane (parameters) make sure it says something like $path\$file -full ) which helps to optimize what should be on screen. If you don't know what all the game is drawing, try gl_wireframe 2, that will show you outlines of everything the game thinks it can "see". If there's something you shouldn't be seeing but are, consider blocking that line of sight with something (e.g. it's drawing a whole room you're not even in? make the hallway twistier!)

Finally if you have lots of multi-sided cylinders and other crap in your map, you might want to raise them 1 unit off the ground (if the player can't really get to 'em) or make them func_wall (if the player can) by clicking the "toEntity" button and selecting func_wall.

whew. I know that's a lot to take in all at once. Maybe I'll punch up a tutorial on r_speeds in general that's a bit easier to read. In the meantime, ask anything you want if you're at all confused. Again, for your first map you don't REALLY need to worry about it, but definitely start desigining in the future with low r_speeds in mind.