I can reproduce this locally on Ubuntu 11.04 -- the worst artifacting goes away if I remove the '-sharpen' (!?!)

Striped output with options as per MW default:

convert \
-quality 80 \
-define jpeg:size=200x289 \
Világosi_Gábor.jpg \
-thumbnail '200x289!' \
-depth 8 \
-sharpen 0x0.4 \
-auto-orient \
out-striped.jpg

Non-striped output with the sharpen removed:

convert \
-quality 80 \
-define jpeg:size=200x289 \
Világosi_Gábor.jpg \
-thumbnail '200x289!' \
-depth 8 \
-auto-orient \
out-ok.jpg

$ convert --version
Version: ImageMagick 6.6.2-6 2011-03-16 Q16 http://www.imagemagick.org
Copyright: Copyright (C) 1999-2010 ImageMagick Studio LLC
Features: OpenMP

I can work around this locally by opening and re-saving the full size image in Gimp.

The original file has 4 color components and may be some sort of CMYK; that might be confusing things in ImageMagick which are optimized more for RGB and RGBA:

$ djpeg -verbose -debug Világosi_Gábor.jpg
Independent JPEG Group's DJPEG, version 8b 16-May-2010
Copyright (C) 2010, Thomas G. Lane, Guido Vollbeding
Start of Image
Miscellaneous marker 0xe1, length 6494
Miscellaneous marker 0xed, length 15496
Miscellaneous marker 0xe1, length 6463
Adobe APP14 marker: version 100, flags 0x4000 0x0000, transform 2
Define Quantization Table 0 precision 0

1    1    1    1    1    1    1    1
1    1    1    1    1    1    1    1
1    1    1    1    1    1    1    2
1    1    1    1    1    1    2    2
1    1    1    1    1    2    2    3
1    1    1    1    2    2    3    3
1    1    1    2    2    3    3    3
1    1    2    2    3    3    3    3

Define Quantization Table 1 precision 0

1    1    1    1    2    3    3    3
1    1    1    2    3    3    3    3
1    1    1    3    3    3    3    3
1    2    3    3    3    3    3    3
2    3    3    3    3    3    3    3
3    3    3    3    3    3    3    3
3    3    3    3    3    3    3    3
3    3    3    3    3    3    3    3

Start Of Frame 0xc0: width=531, height=768, components=4

Component 1: 1hx1v q=0
Component 2: 1hx1v q=1
Component 3: 1hx1v q=1
Component 4: 1hx1v q=0

Define Restart Interval 67
Define Huffman Table 0x00

0   0   6   2   3   1   0   0
0   0   0   0   0   0   0   0

Define Huffman Table 0x01

0   0   6   3   1   1   1   0
0   0   0   0   0   0   0   0

Define Huffman Table 0x10

0   2   1   3   4   1   3   3
2   3   3   3   2   6   9 117

Define Huffman Table 0x11

0   2   1   3   2   4   4   3
5   4   4   4   6   6   5 109

Start Of Scan: 4 components

  Component 1: dc=0 ac=0
  Component 2: dc=1 ac=1
  Component 3: dc=1 ac=1
  Component 4: dc=0 ac=0
Ss=0, Se=63, Ah=0, Al=0

PPM output must be grayscale or RGB

Might be related to bug 24854. That is also about issues with CMYK

Fixed as well? I can't see the original problem as the screenshots were deleted and all seems fine now.

Jup, fixed as well.