considerable, major, serious
There is considerable dispute over the precise definition of ‘social class’ as a term.
The incident sparked off a major dispute between the two countries.

minor, petty
acrimonious, bitter, heated
damaging (BrE)
continuing, lengthy, long-running, long-standing, ongoing, protracted
outstanding
He proposed a negotiated settlement of the outstanding disputes between the two countries.

public
international, local
internal
There were lengthy internal disputes between the two wings of the party.

custody (esp. AmE), domestic, family, marital
industrial (esp. BrE), labour/labor (esp. AmE), pay (esp. BrE)
border, boundary, land, territorial
jurisdictional
a jurisdictional dispute between the Army and the CIA

legal
contract, contractual, patent
ideological, political
commercial, financial, trade
doctrinal, religious, theological

cause, lead to, provoke, spark
one of the many factors that led to the dispute

engage in, enter, enter into
be drawn into
Governments are often drawn into disputes about matters of public taste and decency.

be embroiled in, be engaged in, be involved in
They became embroiled in a dispute with their competitors.

deal with, handle
Police have difficulties in dealing with domestic disputes.

adjudicate, arbitrate, arbitrate in (BrE), decide, mediate, mediate in (BrE)
The purpose of industrial tribunals is to adjudicate disputes between employers and employees.

end, resolve, settle, solve
lose, win
avoid, prevent
be open to
His theories are open to dispute (= can be disagreed with).

arise, begin, erupt, occur
No one could remember exactly how the dispute had arisen.

escalate
concern sth
disputes concerning environmental protection

involve sb/sth

beyond dispute
The matter was settled beyond dispute by the court judgment (= it could no longer be argued about).

in dispute (with)
The actual sum of compensation due is still in dispute (= being argued about).
The employees have been in dispute with management for three weeks.

under dispute
the matters under dispute

dispute about, dispute over
dispute among
The exact relationship between the two languages is a matter of dispute among scholars.

dispute as to
There is no dispute as to the facts.

dispute between
a long-standing dispute between the families over ownership of the land.

dispute with

a matter, point, subject, etc. of dispute
the resolution of a dispute, the settlement of a dispute

hotly, strongly, vigorously
The effectiveness of this treatment is still hotly disputed.

can
No one can dispute the fact that men still hold the majority of public offices.

Dispute is used with these nouns as the object:
allegation, assertion, authenticity, charge, claim, contention, election, fact