Are there any other examples of English words that contain letters not found in the standard English alphabet?
If for “English words”, one counts terms that appear in the Oxford English Dictionary, then yes, there are a very great many such words. Here are just a few examples of the sorts you will find there:
Allerød fête Niçoise smørrebrød
après-ski feuilleté piñon soirée
Bokmål flügelhorn plaçage tapénade
brassière Gödelian prêt-à-porter vicuña
caña jalapeño Provençal vis-à-vis
crème Madrileño quinceañera Zuñi
crêpe Möbius Ragnarök α-ketoisovaleric acid
désoeuvrement Mohorovičić discontinuity résumé (α-)lipoic acid
Fabergé moiré Schrödinger (β-)nornicotine
façade naïve Shijō ψ-ionone
As you see, a great many English words are spelled with letters outside the A to Z set. Just how fussy you are when using these depends in some part on your audience, your input mechanism, and your own care in attending to such details. In modern software, there is no excuse not to use the full character set available to you, but sometimes data may only be entered on a typewriter-style keyboard, lacking all such niceties.
About such things, Robert Bringhurst says the following on pages 179–182 of The Elements of Typographic Style, version 3.2.
(TL;DR: For the summary, skip to the part I’ve editorially set in bold and bold italics, and the paragraph immediately following it.)
9.1 The Hundred‐Thousand Character Alphabet
It is often said that the Latin alphabet consists of 26 letters,
the Greek of 24 and the Arabic of 28. If you confine yourself to
one case only, a narrow historical window and the dialect in power,
this assertion can hold true. If you include both caps and
lower case, accented letters and a global set of consonants and vowels —
á à â å ã ä ą ă ā æ ǽ ç ć č ð đ é ł ñ ň ņ ő š ș þ ű ū ŵ ý ž ź ż
and all the rest — the Latin alphabet is not 26 letters long after all;
it is closer to 600 and able to increase at any time. The alphabet
that classicists now use for classical Greek, with its long parade
of vowels and diacritics — ά ὰ ᾶ ἀ ἃ ἅ ἆ ἁ ἅ ἃ ἇ ᾷ ᾇ, and so on — is
modest by comparison: fewer than 300 glyphs altogether.
To the 600‐character globalized Latin alphabet, mathematicians,
grammarians, chemists, and even typographers are prone to make additions:
arabic numerals, punctuation, technical symbols, letters borrowed from
Hebrew, Greek, and Cyrillic, and, where the letterforms require or invite
them, a few typographic ligatures and alternates as well. There is no
hope at this stage of counting the number of sorts or glyphs precisely,
but the total is clearly over a thousand.
At the end of the eighteenth century, an English‐speaking hand
compositor’s standard lower case had 54 compartments, holding roman or
italic a to z, arabic numerals, basic ligatures, spaces, and punctuation.
The upper case had another 98, containing caps and analphabetics. That
total, 98 + 54 + 152, is the English‐speaking hand compositor’s minimum
basic allotment. When more sorts are required, as they very often are,
supplementary cases are used. Two pair gave 304 compartments; three pair
give 456; four pair gave 608. How Gutenberg’s cases were arranged we do
not know, but we know how big they were. He used not 26 but 290 different
sorts, in one face and one size, in an unaccented script, to set his
42‐line Bible. The Monotype machine, built five centuries later, with 255
(later 272) positions in a standard matrix case, had fallen only a little
Early computers and e‐mail links were, by comparison, living in
typographic poverty. The alphabet they used was the basic character set
defined by the American Standard Code for Information Interchange, or
ASCII. Each character was limited to seven bits of binary information, so
the maximum number of characters was 2⁷ = 128. Thirty‐three of those were
normally subtracted for control codes, and one was the code for an empty
space. This leaves 94: not even enough to hold the standard working
character set of Spanish, French, or German. The fact that such a
character set was long considered adequate tells us something about the
cultural narrowness of American civilization, or American technocracy, in
the midst of twentieth century.
[ . . . ]
Few of us may need (and few may want to memorize) 100,000 characters.
Typographers working Chinese have often mastered 20,000; those who work in
Korean learn 3,000 or more; most literate humans learn a thousand characters
or fewer. Yet authors, editors, typographers, and ordinary citizens who
just want to be able to spell Dvořák, Miłosz, Mą’ii, or al‐Fārābī, or to
quote a line of Sophocles or Pushkin, or the Vedas or the Sutras or the
Psalms, or to write φ ≠ π, are beneficiaries of a system this inclusive.
So is everyone who want to read their e‐mail in an alphabet other than
Latin or a language other than English.
There may also never be a font of 100,000 well‐made characters designed
by one designer. But good fonts with well over ten thousand characters,
keyed to the Unicode system, are now readily available. Computer operating
systems now support them. More importantly, fonts for particular symbol sets
and alphabets can be linked and tuned to one another by adjusting weight,
letterfit and scale. This kind of typographic diplomacy is a task of some
importance — and when character sets are joined in this way, sharing
typographic space whether or not they are all on one font, Unicode can serve
as a coordinating mechanism.
Unicode is relatively new, but many of the resources it catalogues are
ancient. Composition software, communication links, and keyboards are just
starting to catch up.
As Bringhurst says, it’s about inclusiveness — and software is only just now starting to catch up with what the original typesetters, let alone manuscripts, were able to do with perfect ease.