"now" shortcut?
 

In the desktop version of OmniFocus I can type 'now' into a date field, which I use a lot in the Start-Date field for keeping track of when I entered tasks. Is there a way to do this in the iPad-(or iPhone-)app as well?

Why not let OmniFocus keep track of when you entered the task? It already does so, in the Added field. The iOS apps don't show it directly, but you can make perspectives that sort/group by Added, and they will work on iOS.

I've never found a way to automatically spin the date-picker wheels to the current time, it always does either the default due time or in the case of the start time, midnight. I've always found the latter behavior inexplicable; very few tasks really should become active at midnight. An option to set a default start time (just like the default due time, or the ability in forecast view to specify limits on the times displayed in the calendar) would save the population of OF users (on all platforms) a lot of time spent needlessly fiddling with dates!

That would be an option, but the way I work is when I do something on a task but don't finish it, I'd like it to show up at the bottom of my task list. That is, the 'Added' time stamp would need to be updated to the current time.

Just realised there's also a 'Changed' time stamp that I could use...

The only reason this doesn't work right now is that I dumped my old list from Things into OmniFocus, so the majority of my tasks has a 'changed' or 'added' time stamp that's different from the last time I actually worked on it. But once I've touched everything in the course of working my list, that should be automatically corrected. Thanks for the hint!

Okay, I see what you are doing. Probably the easiest thing to do is grit your teeth and spin the time dials. When I work on long tasks without completion, I either update the start date to the next day when I decide I've done enough work on it for now, or in the case of something where I need a marker of my progress, I'll create a new child action under the original describing where to resume, and put the appropriate start date on that. I only do the latter approach where I need the marker, because it is clearly more effort than bumping the start date.

Another approach is to use a perspective that groups by start date. Refer to that to look for work that has been started but not yet completed. You could have the sort inside the groupings be by due date, context, project or maybe date changed, depending on what makes most sense for your needs. Grouping on the iOS apps works a bit differently than on the Mac; when grouping by date, the groups always cover only one day, unlike on the Mac where the groups get larger as you move away from the present into past or future.

Yes, I've created a perspective sorted and grouped by change-date, that works just as I would like.

I think I like the grouping as on the Mac best, larger groups when you move further away from today. On the iPhone it's a bit inconvenient, because you can't collapse the list as on the iPad. Would be nice to have the iPhone-UI consistent with the iPad-way of grouping by date!