Does the Ubuntu image I just downloaded already have all the latest patches and bug fixes included?

I downloaded 12.10 a day after it was released. It is a little buggy in my system - shows the errors such as a problem has occurred frequently. The developers probably have fixed most of the issues by now. So I was wondering if I was to download a fresh copy of the distribution from ubuntu.com, will the distribution have all the bug patches and updates integrated? Or will I have to run update again to install the patches separately?

Once a new version of Ubuntu is released, all of the patches which have been released since the disk images were made will not be incorporated into them the next time you download them. The disk images made available for download at ubuntu.com are pretty much final. Instead, the patches are meant to be applied after installation by running updates, much like what ImaginaryRobots said in their answer. So long as Ubuntu is kept updated, you can be sure that the latest patches for your package versions are already applied.

A semi-exception to the rule is LTS releases, which include several point releases (i.e. 12.04.1, 12.04.2, etc.) after the initial release for the LTS is made, and a new image is built for each point release containing all of the updates released up to when it was built. This is due to the longer support period for LTS releases so you have fewer updates to install after download.

Daily images for the current development version of Ubuntu include all the latest patches and revisions for the newest packages as of the day you downloaded them - but these are made only for unstable versions of Ubuntu which haven't been released yet, and you are likely to run into lots of bugs if you try using them. Similar to official stable releases, these daily images can then also be kept up to date just by running updates.

The only reason why you might want to reinstall Ubuntu, typically, is to "fix" a broken system, or start over with a fresh install. If you plan on using the same version though, you likely won't need to download a new image - just run updates after everything's back in place.

You do not need to re-download and re-install Ubuntu to get updates and bugfixes - simply open the dash and search for Software Updater, and run it. It should run automatically for you on a schedule.

You can make sure that updates are installed weekly by following the instructions here:

https://help.ubuntu.com/community/AutoWeeklyUpdateHowTo

@WarriorIng64's answer above answered my question but I couldn't find any reliable document to verify it. So I asked the question in #ubuntu IRC channel and got comments from peers confirming WarriorIng64's answer - "Patches are NOT integrated into the main build".

I'm pasting the IRC chat transcript here.

<ME> does the ubuntu image i just downloaded has all the patches released so far
<Nice Guy 1> does not, but it does offer installing updates rightaway, or even during the install I believe
<Nice Guy 2> only development version 13.04 has a daily build

That's all.