In the course of the past few years I have learned a great many things about web design. I am a site designer so would like to present to you a few facts about how your new website is going to look and things that will effect it that are outside of your direct control.
Browser type: Depending on what browser you are using, the site will appear differently. There is really no way to avoid this. While most browser types are fairly compatible with each other, they are not consistent in their display. For example a site may look perfect in Internet Explorer, but it will look bit different in Netscape, Fire Fox or Opera. This cannot really be avoided, short of paring the site down to bare essentials and must be expected.
Operating system: Dependent on the machines operating system and how it's set up will effect it as well, for example font types. One can use a font you dearly love, that say everyone with Windows 98 should have as part of the basic package. However, those font packages are not constant from year to year or model to model. What you had in 98 you may not have in ME or XP. Your site that looked fine, now looks funny as the fonts are all wrong once you upgraded your operating system.
Your site design has not changed, but your font files may have. If you don't happen to have the font you used on the new opt system, your browser will default to whatever is set up for default, typically things like arial or times new roman. This change of font availability can also be why it looks odd on your friends machine, but looks just fine on yours. You have the right font, they do not. It's one of the reasons why good design picks fonts that just about any opt system has, saving the fancy stuff for images.
Colors and effects: If for example, there are things like table borders or page transitions etc., very nice and colorful effects. However, most of these effects are proprietary, meaning will only work for IE, being the most common. These effects will degrade, meaning not show up in other browsers. There is nothing your designer can do to force this, it's a browser difference that is unavoidable.
Monitor size: The one thing that will really effect how your new site appears is what size and resolution of monitor you are viewing it on. It's one reason you will still see from time to time, " This site best viewed on IE at 800 by 600 " or something like it. It was an attempt to tell you that, if you want it to view exactly as intended that's the monitor size and browser to do it with. This is currently frowned on and it's dropping out of use. But it brings to mind the central point, that monitor size can make massive changes in the display. Now you can force the site to display in X size no matter what. I don't recommend it however.
By forcing it to display as X pixels wide or tall, no matter what, it will look fine on the monitor size intended for it but the first monitor you see it on that's larger or smaller it's going to look different. Whole lines will move, the main body might reduce to a tiny strip down the middle or blow up and force a side scroll to see it. Even with the best of design this can happen, but forcing it to X size and only X size I can promise you it will happen.
Good design will allow for this and be flexible, by using a percentage of window for your tables and the like, rather than a fixed size. This makes allowances for the monitor type and size it's being viewed on, but it WILL make it look different from type to type. This is good design.
Your designer didn't make an error and make the font too large or too small all of a sudden when you see your new site for the first time on someone else's monitor. It's the monitor itself that is forcing those changes in view. The site itself has not changed. You almost cannot design a page that will look perfectly the same no matter what monitor type you see it on, there will be some differences.
Something else to consider.. personal preferences : Dependent on the persons preferences, they may have their browser set to display larger fonts, or high contrast colors for example, these are personal choices that anyone can make for their display, and has nothing to do with the sites design.
Images: You may send your designer fabulous images, however expect them to change somewhat. In web design one has to compare file size of image VS its load time and display, partially for a business site. Good design may demand that the images be made web ready, which will degrade their quality somewhat. This is not an error, it's good design work, as high quality, meaning large file sizes and web work do not go together for speed of download. The standard for web work is 72 pixels per sq. inch, anything more than that and your file size increases dramatically. Just for comparison realize your average photo is some 4000 to 9000 per. Making the site a turtle is not good design, so the quality of images will have to be sacrificed to a degree.