Hypothyroidism usually occurs in older adults, 5 times as often in women!
It can happen because of an autoimmune or disease process, or a lesion in
the pituitary.  Another form is Hashimoto's disease, an autoimmune
thyroiditis, primarily in women between 30 & 50.  One other form is nontoxic
goiter, which commonly occurs at puberty, during adolescence or pregnancy.

The first symptoms noticed are fatigue and lethargy :)  A gradual slowing of
mental and physical function begins and other symptoms affecting, skin,
hair, nails, joint achiness, weight gain etc.  With nontoxic goiter, an
enlarging of the thyroid gland appears to try and compensate for decrease in
thyroid hormones.

Annecdotal: My daughter developed hypothyroidism after her second baby.  She
just thought she was tired because she had a baby!  No problem with milk
supply at all.  She definetly had a fat neck.  Went for tests etc. and has
been on thyroid ever since (13 years).  They played a lot with her dose
during her 3rd pg.  Had problems keeping thyroid levels stable.  She had no
problems nursing 3rd baby on thyroid.  Interestingly her paternal
grandmother had classic hypothyroidism around age 65.  Her 1st cousin also
developed hypothyroidism after birth of her only child (wasn't BF so no info
about milk supply).  Her brother developed hypothyroidism at age 22. His is
more severe than either of the girls.  I know we're a weird family. :)

So, early symptoms of hypothyroidism are fatigue and lethargy.  Early
symptoms of depression are fatigue and lethargy.  Postpartum causes hugh
flux in hormones, up and down like a roller coaster.  Early motherhood
causes fatigue.
I think blood tests of thyroid function are a fairly easy place to start to
sort this all out if it has become a major problem.  Riordan and Auerbach
state that hypothyroidism without replacement impairs milk supply.  Lawrence
states that there is no contraindication to taking thyroid and BF, because
thyroid is naturally present in breastmilk.