You obviously have made the halftoning with a preset line pattern.
Halftone screen unfortunately tries to keep the result averagely right by making 1 px steps forth and back along the line edges. In addition your image can have noise which increases the unwanted effect by making steps to places where a noiseless image wouldn't need them.
What to do:
Reduce the noise as much as you see acceptable without blurring the image. Noise removal tricks are different case, so I do not show them. I have a few noise removal plugins, Photoshop's Camera Raw has one and there's also in filters Smart Blur and remove noise.
If you have a low resolution image you must lift its pixel dimensions. Use a resizer which is designed to keep sharp edges without increasing blurriness like normal image scaling in Photoshop. I have used Smilla Enlargener (=free) and On1 Resize (=commercial) which both do good job. The latter knows also CMYK colors and transparency.
Remove the image background with clean lasso or clipping path and insert flat noiseless single color background. The background should have good contrast at the edges of the main image object. Then at least the background would be a 100% problem free area.
You must adjust your image to have exaggerated contrast. Half-toning doesn't provide much separate greyshades, so faint details and too low contrast borders can totally vanish.
You can calculate how many greyshades you can have. The line widths must be full pixels. If you have possible linewidths say 0,1,2,3,4 or 6 pixels you have 7 different greyshades.
1 pixel steps at the edges of the generated half-toning lines are not especially much if you have enough greyshades, say more than 10. That means you must have big enough pixel dimensions before applying the halftoning - I mean for ex. more than 1500 px high portrait. If you have it you can well smooth those 1 px steps.
Convert the bitmap image back to RGB and paste it to Illustrator. There do Live Trace to Black and White. Ignore White and search for good other tracing settings. If your pixel dimensions are high enough you can well allow some tracing error in pixels to get smoother paths.
The image of a recently again popular playful smiling boy has got the said noise reduction, resolution lift and a new simple background.
The resolution is lifted to about 500% (=from 400px wide to 2000 px wide) with Smilla Enlargener. The background removal and inserting the new solid one are done after lifting the resolution for best sharpness.
It's possible that sometimes you must insert a stroke or adjust brightness and contrast locally to have border between the main image object and its background. I succeeded to find a good greyshade for the background. The background greyshade is mostly far enough from the object edge greyshade.
Halftoning in Photoshop gives these crunchy lines:
Tracing in Illustrator smooths everything:
The whole portrait looks accurate. I had about 25 greyshades, so the smoothing has not spoilt the result: