I'm not certain what to make of the recent discovery of bundles of cash in the Karmapa Lama's monastery. On the one hand, there's been rumors for ages about him being a Chinese plant. On the other, dubious accounting practices and a general air of venality are very usual among the Tibetan monastic community, both in China and outside. I was once helping run a Buddhist environmental conference in Mongolia, where the first priority of the Tibetan lamas (Chinese-aligned) was to go to the market and buy up as many endangered species' parts "for men's health" as possible. And there's certainly a ton of money flowing into Dharamsala from various sources. So it might just be regular old corruption rather than espionage.
The Dalai himself is genuinely saintly, albeit that some of his proclamations get notably tinted for different audiences (such as his position on homosexuality, which is forgiveable given the frequency of abuse of young monks in Tibet). But his court's full of chancers (both Western and Tibetan), and the Tibetan exile community is even more fractured and bitter than most exile communities.
Quite apart from the nationalist disputes (reconcile with China? fight to the death?), Tibetan Buddhism's not particularly united. The Dorje Shugden controversy has been running for ages, for starters, and incarnation disputes are common - there's a whole bundle of minor reincarnees, and a lot of dubious "wills" get discovered related to where the next incarnation will be found/who should look after the money in the meantime.