Strangely enough, when I don't check Variable line widths for the export of the SWF file, the problem with the "frozen last frame" doesn't occur. However, I do really want those lines to be of variable width.
Another problem seems to be that the SWF files play back significantly slower than the QT file. This rules out any successful attempts to synchronize sounds in the SWF files. I guess if I would own Macromedia Flash or a similar authoring tool, I could solve this problem by trimming the file size of the SWF file and put some pre-loader in it. But the SWF files exported by Moho are not "web ready" it seems.
It turns out there is a bug in some cases if you render one frame and then save it out as PNG. If you want to redner just one frame as PNG, the workaround is to use the Export Animation menu command, select the PNG format, and set the start and end frames to the same number - the one frame you want.