Notice after upgrading from drupal 6.20 to 7.0

Yep, me too. Haven't been able to resolve it yet.

Here's the function and line 749 is a variable rebuild.
$variables = array_map('unserialize', db_query('SELECT name, value FROM {variable}')->fetchAllKeyed());

/**
* Load the persistent variable table.
*
* The variable table is composed of values that have been saved in the table
* with variable_set() as well as those explicitly specified in the configuration
* file.
*/
function variable_initialize($conf = array()) {
// NOTE: caching the variables improves performance by 20% when serving
// cached pages.
if ($cached = cache_get('variables', 'cache_bootstrap')) {
$variables = $cached->data;
}
else {
// Cache miss. Avoid a stampede.
$name = 'variable_init';
if (!lock_acquire($name, 1)) {
// Another request is building the variable cache.
// Wait, then re-run this function.
lock_wait($name);
return variable_initialize($conf);
}
else {
// Proceed with variable rebuild.
$variables = array_map('unserialize', db_query('SELECT name, value FROM {variable}')->fetchAllKeyed());
cache_set('variables', $variables, 'cache_bootstrap');
lock_release($name);
}
}

foreach ($conf as $name => $value) {
$variables[$name] = $value;
}

return $variables;
}

I do not have any additional modules installed 7.0. In 6.20 I had:

Category Status Module Version
Administration 1 Actions permissions 6.x-1.10
Administration 1 Admin Role 6.x-1.3
Administration 1 Administration menu 6.x-1.6
Core - Optional 1 Aggregator 6.19
Other 1 Backup and Migrate 6.x-2.4
Other 1 Better Formats 6.x-1.2
Core - Optional 1 Blog 6.19
Core - Optional 1 Blog API 6.19
Calais 1 Calais 6.x-3.5
Calais 1 Calais API 6.x-3.5
Calais 1 Calais Tag Modifier 6.x-3.5
Spam control 1 CAPTCHA 6.x-2.3
Chaos tool suite 1 Chaos tools 6.x-1.8
Other 1 CKEditor 6.x-1.2
Core - Optional 1 Color 6.19
Core - Optional 1 Comment 6.19
Core - Optional 1 Contact 6.19
CCK 1 Content 6.x-2.9
Core - Optional 1 Database logging 6.19
CCK 1 Fieldgroup 6.x-2.9
Core - Optional 1 Forum 6.19
Core - Optional 1 Help 6.19
Spam control 1 Image CAPTCHA 6.x-2.3
User interface 1 jQuery UI 6.x-1.4
Core - Optional 1 Menu 6.19
CCK 1 Node Reference 6.x-2.9
CCK 1 Number 6.x-2.9
CCK 1 Option Widgets 6.x-2.9
Core - Optional 1 Path 6.19
Other 1 Pathauto 6.x-1.5
Core - Optional 1 PHP filter 6.19
Core - Optional 1 Ping 6.19
Core - Optional 1 Profile 6.19
RDF 1 RDF 6.x-1.0-alpha8
Spam control 1 reCAPTCHA 6.x-1.5
Spam control 1 reCAPTCHA Mailhide 6.x-1.5
Core - Optional 1 Search 6.19
Other 1 ShareThis 6.x-1.8
Other 1 Skinr 6.x-1.6
Core - Optional 1 Statistics 6.19
Other 1 Strongarm 6.x-2.0
Core - Optional 1 Syslog 6.19
Taxonomy 1 Tagadelic 6.x-1.2
Taxonomy 1 Tagadelic all block 6.x-1.2
Views 1 Tagadelic Views 6.x-1.2
Core - Optional 1 Taxonomy 6.19
CCK 1 Text 6.x-2.9
Other 1 Token 6.x-1.15
Other 1 Token actions 6.x-1.15
Core - Optional 1 Trigger 6.19
Other 1 Twitter 6.x-3.0-beta3
Other 1 Twitter actions 6.x-3.0-beta3
Other 1 Twitter Post 6.x-3.0-beta3
Core - Optional 1 Update status 6.19
Core - Optional 1 Upload 6.19
CCK 1 User Reference 6.x-2.9
User interface 1 Vertical Tabs 6.x-1.0-rc1
Views 1 Views 6.x-2.12
Views 1 Views Bulk Operations 6.x-1.10
Views 1 Views Send E-mail 6.x-1.x-dev
Views 1 Views UI 6.x-2.12

I found this thread http://drupal.org/node/49694
But the code has changed a bunch for D7 so I am not sure how to apply it.

My error:
Notice: unserialize() [function.unserialize]: Error at offset 2 of 8 bytes in variable_initialize() (line 748 of /home1/explore8/public_html/2tim/includes/bootstrap.inc).
Doesn't help because the SQL:
select name, length(value), value from variable where length(value) = "8";
finds 100s of variables

I'd rather not just cover up the error as suggested, or it might bite me later.

Found it. There is now a module to find bad variables http://drupal.org/project/variablecheck
Install it, go to your status report, run the variable check, tell some module developers about bad variable where appropriate,
then using phpmyadmin, click on variable table, search tab, look for your variable using %like%, delete where you can afford it