@neota: Thank you for your suggestions. I'd love to see it with your suggestions, however, I cannot see how they could be done. In the same order as your points

• I agree I could take that light-gray line out from the left face of the block. I cannot use any more colours around the tile borders beneath the block, they fill the full compliment of colours
• There is only 1 more gray colour, which is darker than both the shadow and the tile, "AAing" the blue line with it just makes it look crap and those are the only two blues available
• Again, all the blocks contain their full colour usage, besides, there are no more greens (which is why the "shading" was brown)
• There are the odd blocks I can add the orange around the edge of the balloon (some use the full colour allocation), but there are no colours which can be used to AA inside the balloon. Suppose I could have tried some dithering, but I didn't think of that at the time.
• Printing was intentional

reminds me of Reckless Rufus.

anyway there definitely is space for more AA, even considering the restrictions.

• Under the rising block (left side) --both along the bottom edge and along the tile border beneath it.
  
• The edge of the grey tile that is shadowed by the character
  
• Bottom-right edge of the character
• Some of the balloon edge
• On most of the printing (but I could understand why you might not want it there)

The downside to multicolour mode on the C64 is that each "pixel" is actually two pixels wide, so it's not that easy to do circles. The picture is made up of 8x4 blocks (8x8 pixels), but each block can only have a maximum of 4 colours, which makes AAing pretty hard. That and there is only 16 colours in the C64 palette.

is everything supposed to be so sharp