Using some zoom shouldn't affect image quality... at least not as long as you are somewhere within the central 50%-70% of the zoom range. If you are way out at the extremes of the zoom range you MIGHT see a slight softening.
With a 120" screen, you should be sitting more than 10 feet from the screen... I'd say at least 11' from the screen. Sitting too close can reveal pixel structure and/or screen texture, both of which can soften the appearance of images. Also, you want to be sure the Sharpness control isn't softening images. Some do, some don't - you really have to have a sharpness evaluation pattern to be able to tell if your Sharpness control's correct setting is 0 or some other setting. Some sharpness controls have settings that range from no sharpening to way too much sharpening -- the no sharpening setting is the only correct setting. Other sharpness controls have the "no sharpening" point somewhere in the middle of the settings range and if you go lower than that, the images get softer. On the other hand, some Sharpness controls do nothing at all (so Marketing gets their sharpness control and display owners can't do any harm to the image by using an inappropriate sharpness setting).
Some screen materials are "sharper" than others as well. And, of course, the optics in the projector are also an important factor.
If you are resolving the single pixel pattern in a multi-burst pattern. Multiburst patterns have alternating black and white lines, usually vertical, sometimes horizontal, the groups of lines are 1 pixel wide in the finest part of the pattern, next is 2-pixel wide alternating black & white lines, then (usually) 4-pixels wide... the sets of lines with more than 1-pixel per line will always resolve properly. If the single-pixel lines aren't resolving, you probably haven't selected an output mode from the projector that provides 1-to-1 pixel mapping (a small amount of zoom is applied instead and that interferes with the projector achieving maximum image detail. If that's your problem, you need to find a 1-to-1 pixel mapping mode so that you are resolving single-pixel wide alternating black and white lines. If you have the DVE disc, their pattern is a 1x1 pixel checkerboard with white and black pixels in a checkerboard patter (the same pattern also has 2x2 pixel checkerboard, along with even coarser checkerboard patterns... same thing would apply when using this pattern also... if you can't see the 1x1 pattern, you aren't getting maximum image sharpness. Be aware that some LCD projectors can't resolve the single-pixel line or checkerboard patterns due to internal high-frequency filtering. If this is the case, the DVE single-pixel checkerboard pattern might look black or gray or some pastel color due to the projector not being able to fully resolve a full 1920x1080 pixels.
To get the best image sharpness the projector's optics can produce you should be somewhere in them middle of the focus range and zoom range rather than being at an extreme. Keystone adjustments should be turned off also... those will kill resolution of fine detail also. Limitations in the quality of the optics can show up as lack of contrast in images that gives the impression of softness even if the multiburst or single-pixel checkerboard patterns look OK.
It's a fairly big topic. Optics and imaging systems are important and some of what you get when you go for more expensive projectors is improvements in optics of the projector. The first thing I'd do is find out if the projector resolves 1920 pixels horizontally (with a vertical line pattern or the 1x1 checkerboard pattern) and that it is also resolving 1080 lines vertically (with a horizontal line pattern or the 1x1 checkerboard pattern. If it does, none of the settings/setup issues I mentioned here will apply (though the sharpness control MIGHT still have some involvement).
With a 120" screen, you should be sitting more than 10 feet from the screen... I'd say at least 11' from the screen. Sitting too close can reveal pixel structure and/or screen texture, both of which can soften the appearance of images. Also, you want to be sure the Sharpness control isn't softening images. Some do, some don't - you really have to have a sharpness evaluation pattern to be able to tell if your Sharpness control's correct setting is 0 or some other setting. Some sharpness controls have settings that range from no sharpening to way too much sharpening -- the no sharpening setting is the only correct setting. Other sharpness controls have the "no sharpening" point somewhere in the middle of the settings range and if you go lower than that, the images get softer. On the other hand, some Sharpness controls do nothing at all (so Marketing gets their sharpness control and display owners can't do any harm to the image by using an inappropriate sharpness setting).
Some screen materials are "sharper" than others as well. And, of course, the optics in the projector are also an important factor.
If you are resolving the single pixel pattern in a multi-burst pattern. Multiburst patterns have alternating black and white lines, usually vertical, sometimes horizontal, the groups of lines are 1 pixel wide in the finest part of the pattern, next is 2-pixel wide alternating black & white lines, then (usually) 4-pixels wide... the sets of lines with more than 1-pixel per line will always resolve properly. If the single-pixel lines aren't resolving, you probably haven't selected an output mode from the projector that provides 1-to-1 pixel mapping (a small amount of zoom is applied instead and that interferes with the projector achieving maximum image detail. If that's your problem, you need to find a 1-to-1 pixel mapping mode so that you are resolving single-pixel wide alternating black and white lines. If you have the DVE disc, their pattern is a 1x1 pixel checkerboard with white and black pixels in a checkerboard patter (the same pattern also has 2x2 pixel checkerboard, along with even coarser checkerboard patterns... same thing would apply when using this pattern also... if you can't see the 1x1 pattern, you aren't getting maximum image sharpness. Be aware that some LCD projectors can't resolve the single-pixel line or checkerboard patterns due to internal high-frequency filtering. If this is the case, the DVE single-pixel checkerboard pattern might look black or gray or some pastel color due to the projector not being able to fully resolve a full 1920x1080 pixels.
To get the best image sharpness the projector's optics can produce you should be somewhere in them middle of the focus range and zoom range rather than being at an extreme. Keystone adjustments should be turned off also... those will kill resolution of fine detail also. Limitations in the quality of the optics can show up as lack of contrast in images that gives the impression of softness even if the multiburst or single-pixel checkerboard patterns look OK.
It's a fairly big topic. Optics and imaging systems are important and some of what you get when you go for more expensive projectors is improvements in optics of the projector. The first thing I'd do is find out if the projector resolves 1920 pixels horizontally (with a vertical line pattern or the 1x1 checkerboard pattern) and that it is also resolving 1080 lines vertically (with a horizontal line pattern or the 1x1 checkerboard pattern. If it does, none of the settings/setup issues I mentioned here will apply (though the sharpness control MIGHT still have some involvement).