The /ð/ sound is spelled with <th>. The /n/ sound is spelled with <n>, <nn> or <gn>. Sometimes a final /Ɵ/ is voiced when made plural, which is why there is no matching singular forms for the pair oaths/owns.
This is a contrast between a dental fricative and an alveolar nasal continuant, both voiced. It is not a problem.
Since /n/ is a common sound while /ð is rare, the mean density value is low at 0.4%. The list makes 40 semantic distinctions, a loading of 74%.
bathe bane baths barns booth boon booths boons clothe clone clothes clones dither dinner dithers dinners lathe lain lathe lane lathes lanes laths larns lithe line loathe loan loathed loaned loathes loans loathing loaning loathsome lonesome mouthed mound oaths owns scythed signed seethe scene seethes scenes sheathe sheen soothe soon swathe swain swathes swains teethe teen teethes teens tether tenner tethers tenners that Nat that gant thee knee their ne'er these knees they née thine nine though know those knows thou now thy nigh tithe Tyne tithe tine tithes tines whither winner with whin with win wither winner withers winners withy whinny withies whinnies writhe Rhine writhed rind
John Higgins, Shaftesbury, November 2010.