How vulnerable is Linux in general from finger faults from normal everyday Windows users?
Ubuntu – How safe is Ubuntu for “non-geek” users
Security
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Why you're asked for a password
Most software is designed to touch sensitive files, i.e. sensitive to the security of your private data or the systems integrity. This is why software installation is a potential risk and should be validated by a user who knows what he is doing. Even for open source Software you can not be sure that no bad code bits arrive with your percious new audio player until someone checked. And even then something could have been overlooked or packages could be manipulated on the way. Who knows what's hidden in the depth of the program? One user should.
Ubuntu provides a comfortable way of installing software. Software developers can rely on that comfort and make the assumption that synaptic/software center/apt enables them to access these sensitive files. Canonical checks the software repository for bugs and malicious code. But the ultimate responsibility is yours.
If the software in question does not need access to sensitive files, it can (in principle) be installed in the home folder though not in the Ubuntu way. You will for instance have to compile the source code yourself or run a custom install script. Beside the greater efforts of that it has the disadvantage of not allowing other users access to your just installed program (as they have no right to access your home-folder). They will need to installed it a second time. So this way of installation makes no sense in a large scale and in a small scale it's usually easier to type a password than to install software manually.
So that's why Synaptic aaks for a password and why it's good that it does.
Sudoers
If you are really in dire need of having other users install software without password, you can add them to the sudoers list. This however will result in a great security risk. If that doesn't concern you, consider that there a bot networks out there with great resources to break into your computer via Internet. They do this just to add your computer to the net and use it's connection and computing power without your knowledge to do all sorts of illegal stuff. They are not even after your personal data your you for that matter. They just want to hijack your PC. Still not concerned? Really? Then look at the following answer which is a small how-to on the workings of sudoers list:
How to make Ubuntu remember forever the password after the first time
Read that carefully. You could lock yourself out of the system.
The scare is over
So now you have the scare behind you are and taking the matter seriously, I can tell you it's really not that bad. If you trust the people working on your computer, and you don't have programs installed that allow remote access to your system (e.g. an ssh- or ftp-server), then it's really not that dangerous to disable the password stuff. Just don't do it without considering the worst case and think of your private data.
Overlook on the proceedings (don't do this lightly - see text and link above):
# in shell type these commands
sudo su # in case you do something stupid, you'll have a root shell open
select-editor # (optional) will allow you to select text editor
visudo # secure way to open sudoers list
An editor will open ADD a line like this:
confus confusion=(root) NOPASSWD:/usr/sbin/synaptic,/usr/bin/software-center
Syntax explanation: username machine=(usernameToRunCommandAs) command1,command2,.... So the above line allows confus to run synaptic and softwarecenter as root without password query. You will still need to start it with sudo synaptic or gksudo synaptic or put an alias `alias synaptic='sudo synaptic' in your shell profile.
Create a group for users allowed to use terminals, let's say terminalusers. Find the terminal program (use which), for example, xterm. Change its ownership accordingly :
chown root:terminalusers /usr/bin/xterm
Allow execution for the owner, and the group. Deny for others :
chmod 750 /usr/bin/xterm
At this point, using xterm wont be possible unless you're root, or a member of the terminalusers group (add yourself to it, and you'll be able to use xterm). Apply similar settings for other terminal emulators (gnome-terminal is your main one I suppose). Now, this is just another trick : it blocks terminal emulators, not terminals (subtle difference indeed).
In a UNIX environment, terminals are the primary interfaces to the system. Blocking them is very likely to disturb many applications, not only command-line ones. Blocking terminal emulators instead is nothing but a workaround. With good permissions, remember that nothing bad can happen to your machine from a user terminal : it takes root privileges to mess things up.
Note : with xterm, this is said to cause problems with utmp.
Best Answer
From my experience, I would say that once you set up a Ubuntu box properly, normal users won't make it crash easily. My parents are not exactly technical people, and they have been using Linux distributions for years without larger problems (actually they got a Fedora box just now).