After reading up on how this works, I marked a bunch of items (which use user parameters) as active checks. When I did this, items which had the "Store value" field set to "Delta" were suddenly all over the place; it appears that Zabbix was now computing deltas that were several orders of magnitude wrong. My guess is that the delta computation is not normalized with respect to the collection delay; is this by design?
This is Zabbix 1.8.2.
This is Zabbix 1.8.2.