Via google webmaster tools you can ask to have all your urls removed and let google reindex your site completely. Would not advise to do so as it costs a lot of time to get reindexed and you will loose all your links for the time being.
If googlebots spider your site/forum on regular basis you will get reindexed soon enough.
When we moved from vbulletin (with vbseo) to xenforo we decided not to use a script for the change in urls. Lots of 404's the first weeks and a significant drop in visits from google of course but after a few months we are back on the same level as with vbulletin (with new url structure) if not better.
If you change the crawl rate in webmaster tools, it might set off their indexing robot a bit faster. Normally, however, they should be re-indexing you anyway on a basis determined by the popularity of your site, the number of pages and the number of updates you make.
Yes, google keeps track of changes in your pages over time, and if they almost never change, it is likely to crawl the site less and therefore update less.
You should be able to find out more by looking at the google webmaster tools (crawl rate). My site is crawled at the rate of tens of thousands of pages per day, which means google is usually right up to date on indexing it. That is because google knows things change by the minute on Hearth.com